Annual Report 2008 - Fields Institute - University of Toronto

Fields Institute 

for Research in 

Mathematical Sciences 

fields 

Annual Report 2008

Fields Institute 

for Research in 

Mathematical Sciences 

The Fields Institute is a centre of 

mathematical activity in Canada – a place 

where mathematicians from educational 

and research institutions in Canada and 

abroad, and from business, industry, and 

financial institutions, can come together 

to carry out research on problems of 

mutual interest. The Institute provides a 

supportive and stimulating environment 

in which these diverse groups can interact. 

Its goal is to ensure that Canada plays a 

significant role in mathematical discovery 

and mathematical application in our 

modern technological society. 

iii

Institute Profile 2 

Message from the Chair of the Board 4 

Message from the Director 5 

Thematic Programs 

Operator Algebras 7 

Harmonic Analysis 23 

Coxeter Lecture Series 

Jill Pipher 31 

Distinguished Lecture Series 

Uffe Haagerup 33 

Timothy Gowers 35 

Alain Connes 38 

2008 CRM-Fields-PIMS Prize Lecture 

Allan Borodin 39 

Special Events 43 

National Program on Complex Data Structures 52 

General Scientific Activities 

Workshops and Conferences 53 

Seminars 100 

Centre for Mathematical Medicine 107 

Joint Institute Initiatives 112 

Commercial/Industrial Mathematics 

Workshops, Seminars and Courses 119 

Start-Up Firms Fostered by the Fields Institute 125 

Mathematics Education 

Mathematics Education Forum 127 

Outreach Programs and Workshops 129 

Fields Institute Fellows 133 

Contents 

Publications 

Fields Institute Monographs 134 

Fields Institute Communications 135 

Editorial Board 137 

Fields Notes 137 

Governance 

Fields Institute Staff 138 

Board of Directors 138 

Members of the Corporation 139 

Scientific Advisory Panel 140 

Industrial Advisory Board 144 

Principal Sponsoring Universities 145 

Financial Statements 

Donors 149 

Auditor's Report 150 

Financial Statements and Notes 151 

Acknowledgements 159 

1

Institute Profile 

2 

John Charles Fields 

Founded in 1992, the Fields 

Institute is named after 

the Canadian mathematician 

John Charles Fields 

(1863–1932). Fields was a 

pioneer and visionary who 

recognized the scientific, 

educational, and economic 

value of research in the mathematical 

sciences. He is best 

known for establishing the 

premier international prize 

in mathematics–the Fields 

medal–which is considered to 

be the Nobel Prize of mathematics. 

The Fields Institute occupies a building, situated on the 

University of Toronto campus, designed by Kuwabara 

Payne McKenna Blumberg (KPMB) for Fields Institute 

activities. Its purpose is to enhance mathematical activity 

in Canada by bringing together mathematicians from 

Canada and abroad, and by promoting contact and collaboration 

between professional mathematicians and the 

many diverse users of mathematics. The Institute supports 

research in pure and applied mathematics, statistics, and 

theoretical computer science. It also supports collaboration 

between mathematicians and those working in other areas 

such as engineering, the physical and biological sciences, 

medicine, economics and finance, telecommunications, 

and information systems. 

The Institute building is designed to support and enhance 

these varied activities. Office space is provided for up to 

sixty-eight visitors; a supportive staff enables program participants 

to devote their energies to research; and full access 

to the excellent mathematics collection at the University of 

Toronto is provided. 

The primary activities at the Institute are its thematic 

programs, usually one semester in length. These involve 

participants from Canada and around the world, and 

include graduate students and postdoctoral fellows, as well 

as more senior and well-established scientists. The topics of 

thematic programs embrace all the mathematical sciences 

as well as areas in which mathematics is or can be applied. 

Regular workshops, conferences, and graduate courses 

are planned by the program organizers to support these 

goals, while all administrative and non-scientific details are 

arranged by the Institute staff. 

In addition to its thematic programs, the Fields Institute 

supports a wide range of programs of shorter duration 

such as workshops and conferences, short courses, summer 

schools, recurring seminar series, and special lectures. Such 

activities are sometimes held off-site, many of them on the 

campuses of our sponsoring universities. 

The Commercial and Industrial Mathematics Program 

(CIM) acts as a bridge between the mathematics community 

and businesses that benefit from research in the 

mathematical sciences. In this way, the CIM program seeks 

to communicate results in mathematics to the business 

community, and, conversely, to create an awareness among 

mathematicians of the needs of that community. The scope 

of this program includes the medical and health sectors 

through the Centre for Mathematical and Medicine. 

The National Program on Complex Data Structures has 

been a joint initiative of the Canadian mathematical sciences 

institutes, together with the statistical community. 

The goal of this network was to foster nationally coordinated 

projects with substantial involvement of scientists 

working to analyze complex data sets, as well as to establish 

a framework for national networking of research activities 

in Statistics. NPCDS supported workshops designed to 

stimulate such projects and networks. 

The Institute is strongly committed to mathematics 

education. The focus of these efforts is the Mathematics 

Education Forum which holds monthly meetings at the 

Institute to discuss issues of mathematics education at all 

levels. The Forum brings together participants from high 

schools, school boards, faculties of education, mathematics 

departments in universities and colleges, and the private 

sector. One of the major contributions of the Forum was 

the 1998 revision of the Ontario high school mathematics 

curriculum, carried out through a contract of the Fields 

Institute with the provincial Department of Education. 

Later, then deputy director Tom Salisbury chaired the 

Curriculum Council Task Force on senior high school 

mathematics in Ontario. The Fields Math Circles program 

is a new initiative aimed at high school students interested 

in mathematics competitions and problem solving. 

Major funding is provided by the Ontario Ministry of 

Training, Colleges, and Universities and the federal Natural

Sciences and Engineering Research Council (NSERC). 

Our seven principal sponsoring universities are Carleton 

University, McMaster University, the University of Ottawa, 

the University of Toronto, the University of Waterloo, the 

University of Western Ontario, and York University. 

In addition there are twelve affiliate universities: Nipissing 

University, Queen’s University, the Royal Military College 

of Canada, the University of Guelph, the University of 

Houston, the University of Manitoba, the University of 

Maryland, the University of Ontario Institute of Technology, 

the University of Saskatchewan, the University of 

Windsor, Trent University, and Wilfrid Laurier University. 

The Corporate Affiliate Members of the Fields Institute 

are Algorithmics, General Motors, QWeMA Group Inc., 

R2 Financial Technologies Inc., and Sigma Analysis and 

Management. 

Institute Profile 

3

Message from the Chair of the Board 

4 

John R. Gardner 

The DiReCToR’S RepoRT ouTlineS The Many wayS in 

which the past year was another step forward for the Institute 

with respect to its mission of advancing mathematical 

knowledge and developing mathematicians. In my report 

I will comment on three additional dimensions of the 

Institute’s activity that reflect real progress: membership, 

funding and leadership. 

During the 2007-2008 year the Institute welcomed into the 

ranks of its members Trent University and the Royal Military 

College. Our mission is best accomplished when our 

activities reach out to include all our neighbouring mathematical 

communities, especially in Ontario. With these 

additions, almost all Ontario universities are now affiliated, 

in one way or another, with the Fields Institute. 

Strong votes of confidence were received during the last 

year from the Institute’s two primary funding agencies. 

NSERC’s decision to increase its financial support of Fields 

was reflected for the first time during the 2007-2008 fiscal 

year. The decision by the Ontario Ministry of Training, 

Colleges and Universities to extend its funding of the 

Institute for another five years at twice the rate will have a 

profound impact on the strength of future programming. 

We welcome these decisions both for the approval they 

reflect and for their impact on the resources we can put to 

work. 

Leadership. The Institute has been blessed all during its history 

with strong leadership from its Directorate. At the end 

of this calendar year, after four and one half years in the 

chair, Barbara Keyfitz will leave the position of Director to 

go to Ohio State University. The following six months will 

see Juris Steprāns carry the baton as Acting Director, until 

Ed Bierstone steps in as the Institute’s Director. 

Barbara’s contributions to the Institute are enormous. The 

expanded range and increased strength of its activity result 

from her imagination and energy. Her management style 

has kept the Institute moving forcefully along its track in 

good spirits. She has broadened the Institute’s presence on 

the world stage. We owe a great deal to Barbara, and wish 

her and her husband well in their new venture. 

Ed Bierstone, a highly respected mathematician and 

teacher, will take over the Director’s role a little less than a 

year from now. His vision, experience and knowledge of the 

Canadian mathematical scene will all be invaluable to the 

Institute. Ed comes to Fields on secondment from his position 

at the University of Toronto, and it is noteworthy that 

he is spending his 2008-09 sabbatical as a participant in one 

of the Institute’s thematic programs of the year. 

The six month gap between director appointments will 

afford Juris Steprāns the chance to experience the role 

of Director of Fields. The institute has been fortunate in 

having highly capable individuals fill the demanding position 

of Deputy Director, and Juris is no exception. I look 

forward to working with him as he guides the Institute on 

its course. 

John R. Gardner, Chair

Barbara Keyfitz 

The FielDS inSTiTuTe’S annual RepoRT iS The DoCuMenT 

of record of our activities for the year. While more detail 

is available in our Web archives, and while many of the 

ideas generated by the programs reported here will find 

their way into research papers and students’ dissertations, 

the Annual Report is the comprehensive statement of what 

we did – with our time and our resources – for the twelve 

months from July 2007 to June 2008. In its pages you will 

find summaries, most of them written by the participants 

themselves, of all the events that took place within our 

walls, and of all the activities elsewhere to which we lent 

planning advice, funding, and logistical support. We thank 

all the organizers and participants in these events, and we 

are grateful to the contributors of articles for their willingness, 

after the events were over, to sit down and write about 

them. 

In presenting this Annual Report, my last as Director of 

Fields, I want to share with you some professional and personal 

musings on the state of Fields, on institutes in general, 

Message from the Director 

on their role in the career of a mathematician, and on their 

role in my career. This column, adapted from remarks I 

made at this year’s AGM, should be viewed through the lens 

– one that many visitors to Fields have shared – of one who 

has had the time of her life here, but now recognizes that 

the time has come to move on to other things. 

There are three threads to these musings. 

What makes an institute? What does an institute make? 

At times it seems desirable to justify, to possibly skeptical 

visitors, why it is cost-effective to put resources into the 

operation of a building rather than just giving the money 

directly to individual researchers. For there is no doubt 

that our institute is “real’’ and not “virtual’’; our building 

costs real money to operate and our staff earn real salaries. 

In fact, I would argue that one should recognize those 

facets of our operation for what they bring: a building that 

says “Research’’ with every brick and that demonstrates 

to a sometimes unbelieving world that mathematics is a 

dynamic, thriving, research-oriented discipline. And, as 

well, that the research enabled by institutes, collectively, is 

different – in its scope, in its complexity, in its cooperative 

nature – from what individuals typically accomplish within 

their usual routines. 

I ought to justify that by reference to some signal events, 

such as the contribution of a program at Fields to the 

development of the notion of universality in SLE evolution, 

for which Wendelin Werner won the Fields Medal two years 

ago. This is not a unique achievement of Fields, as there are 

similar outstanding stories from CRM, Newton, and other 

institutes. But one doesn’t have to look that high. During 

my career, I benefited from two long-term visits to math 

institutes. The first was a six-month visit to the IMA in 

1989, and the second was to Fields itself in 1993, during the 

first full year of its operation, in Waterloo. The six months I 

spent there with a postdoctoral visitor (supported by Fields) 

helped us start a project that has been the centrepiece of my 

research ever since. So, when anyone asks me whether being 

director of Fields has slowed down my research, I respond, 

“Yes, but it is a small way of repaying some of what the 

Institute did for me.’’ 

An institute is a real place, with a real culture, different 

in so many ways from the everyday world of mathematics 

5

Message from the Director 

departments – that world we love, and always return to, but 

sometimes need to get away from. And things happen at an 

institute that don’t happen at home. I do find that for the 

past four years I’ve felt as though I was living in a fairy-tale, 

and it’s probably a good idea to get back to a less rarefied 

atmosphere. 

Why does a medium-sized country need mathematics 

research institutes? 

The question of measuring the advantages of being the 

home of a mathematics research institute could be phrased 

in a number of different ways, such as, “Why does a large 

province in a medium-sized country need ….?’’ Or “Why 

does Canada need more than one …?” These titles (and 

others like them that you can imagine) were inspired by 

a talk given a few years ago by Louis Chen, founder of the 

Institute for Mathematical Sciences in Singapore, called 

“Why does a small country need….?’’ Of course, mathematically, 

Canada is neither a small nor a medium-sized 

country. Canada is one of only ten (out of 68) members 

of Group V of the International Mathematical Union, the 

highest class of membership. Canada combines, uniquely, 

a large territory, a relatively small population, and a high 

standard of living (high enough to afford the exponentially 

increasing cost of Group V membership). 

Mathematics is also a very international discipline. This is a 

not unique attribute, but it is distinctive. One can specialize 

in Canadian Literature, or in Canadian Botany. But Canadian 

Mathematics? (This has nothing to do with Canada 

-- a focus on US or French Mathematics would be equally 

ridiculous.) But students work on problems given by their 

advisors, and then often look for jobs in the country where 

they received their education. And people talk more to 

their neighbours than to people far away. Without travel, 

it would be hard to keep ideas flowing across borders. So 

there is intrinsic value, whether you are located in a small 

country or in a large one, in finding out what people in 

other places are doing. Our collective budget for travel – 

airfare, accommodation, per diems – is enormous. If we 

were speaking only of economic impact, then I’m sure the 

city of Toronto and Air Canada collect enough from our 

visitors to sponsor a few workshops a year. 

We try, by carefully selecting programs, to optimize 

these travel dollars. We try to make sure that the visitors 

we sponsor bring the most exciting new ideas here, and 

that they are people well-prepared to absorb and carry 

home with them the ideas generated in Canada. I’ve been 

6 

impressed, over and over again, with the value added by our 

Scientific Advisory Panel, with its combination of Canadian 

and international mathematicians. 

Institutes build communities 

It’s been pointed out by scholars more astute than me that 

academic life can be competitive. Perhaps it’s the price 

we pay for academic independence. We compete with 

each other for research grants, for tenure, and for the best 

students. Departments fight turf wars over discipline 

boundaries. Universities argue with each other over ratings. 

Mathematics institutes are little islands of peace in this 

cacophony of trumpet-blowing. I quote Doug Arnold, who 

has just completed his term as director of the IMA in Minneapolis, 

on the role of institutes: “With the mathematics 

institutes, mathematics has gone from being inwardlooking 

and isolated to being central and connected.’’ Doug 

also noted that the climate at institutes is sunny: People 

are happy to be there because they feel privileged to have 

been invited, and because they are getting away from their 

everyday routines. I trust that our visitors take with them 

some of this appreciation for cooperation, for generosity, 

for inclusiveness, and for the pursuit of excellence when 

they leave. 

I know that I will. 

I am profoundly grateful for the opportunity Fields has 

given me to be your director for 4 1/2 years. It has been a 

life-changing experience. 

Barbara Lee Keyfitz, Director

Operator Algebras July–December 2007 

Organizing Committee: George Elliott (chairman, 

Toronto), Dietmar Bisch (Vanderbilt), Joachim Cuntz 

(Münster), Kenneth Davidson (Waterloo), Thierry Giordano 

(Ottawa), Roland Speicher (Queen’s) 

Scientific Advisory Committee: Alain Connes (Collège de 

France and Institut des Hautes Etudes Scientifiques), Uffe 

Haagerup (University of Southern Denmark), Vaughan F. 

R. Jones (Berkeley), Eberhard Kirchberg (Humboldt), N. 

Christopher Phillips (Oregon), and Dan-Virgil Voiculescu 

(Berkeley) 

PROGRAM DESCRIPTION 

During the period July to December, 2007, The Fields 

Institute sponsored a major thematic program on operator 

algebras and their relations with other fields of mathematics. 

This program continued on a smaller scale during the 

period January to June, 2008. 

The program comprised both formal and informal 

aspects – perhaps of equal importance. The more formal 

components have been of three kinds: courses (four regular 

courses at the Fields Institute, and in addition four short 

courses at the Ottawa Summer School); seminars (two 

weekly two-hour seminars during the whole year); and 

meetings – both a number of workshops centred on a single 

theme, with six of these held on site and five organized 

at other locations in Canada, and two general meetings, 

namely, two successive instances of the Canadian Annual 

Symposium on Operator Algebras and Their Applications – 

the 35 th , in Guelph in June of 2007, and the 36 th , in Toronto 

in May of 2008. (This annual meeting, begun by Israel Halperin 

in 1972, may have been the first regular conference in 

a particular field of mathematics. It was of course followed 

by numerous others – not least in the field of operator 

algebras. It might be mentioned that Halperin, a student 

of von Neumann and the last of the pioneers of the subject 

from the 1930s, died a few months before the beginning of 

the program.) 

A notable aspect of the program has been the considerable 

number of longer-term participants, at all levels (senior, 

postdoctoral, and graduate student). Among the younger 

participants, an encouraging number have been women. 

Two Fields Institute Distinguished Lecture Series were 

related to the program. The lectures both of Uffe Haagerup 

(in November, 2007) and of Alain Connes (in May, 2008) 

George elliott 


were closely associated with meetings in which their work, 

and their participation, played an important role. Indeed, 

in the first case there were two meetings, one held shortly 

before Professor Haagerup’s lectures, and one after. In the 

second case, in addition to a workshop held during the 

same week as Connes’s lectures, there were two meetings 

the week before – one in Ottawa and one in Toronto – and 

also one the week after – namely, the Second Canada- 

France Mathematics Congress in Montreal, several sessions 

of which were related to the subject of operator algebras. 

The work of both Uffe Haagerup and Alain Connes 

impinges on the whole of the theory of operator algebras 

– and indeed may be thought of as of such a depth that it 

goes well beyond this field. To put it still more strongly, 

the work of Connes and Haagerup – one should also at the 

same time mention the work of two other mathematicians, 

Vaughan Jones and Dan Voiculescu, also participants in the 

program (and also, on previous occasions, Fields Institute 

Distinguished Lecturers) – takes considerable steps in the 

direction of placing the field of operator algebras centrally 

in mathematics as a whole. Indeed, the work of these four 

mathematicians has exerted considerable influence on a 

number of areas, both of mathematics and of physics. 

Let me summarize very briefly some aspects of the work 

of the four mathematicians just mentioned, and how it 

has influenced the work of others, and in particular work 

accomplished during the Fields program. 

7


Connes’s early work, recognized with a Fields Medal, 

resulted in a definitive analysis of what are now referred to 

as amenable von Neumann algebras (on a separable Hilbert 

space). (A von Neumann algebra is a self-adjoint algebra of 

bounded Hilbert space operators, equal to its bicommutant. 

Amenability is a natural condition, analogous to amenability 

for a group, and indeed equivalent to amenability of the 

unitary group of the algebra, in its natural topology – not 

the norm topology.) The climax of this work (in which 

the work of many others – both around that time and also 

earlier – played a role) was the complete classification, in a 

natural sense, of amenable von Neumann algebras. 

This work led in several directions. It prompted Jones 

to apply similar ideas to the study of subalgebras of von 

Neumann algebras. This in turn led to Jones’s discovery of 

the Jones polynomial, which revolutionized not only the 

theory of knots but also, through the subsequent work of 

Witten and others, large parts of both physics and mathematics. 

(Both Jones and Witten were awarded the Fields 

Medal for this work.) The work of Connes on amenable von 

Neumann algebras also prompted Elliott, somewhat later, 

to consider the class of amenable C*-algebras from a similar 

point of view. (A C*-algebra is a self-adjoint algebra of Hilbert 

space operators which is closed in the norm topology; 

it should be considered together with all its representations, 

not just a given one, and it is said to be amenable if all of 

these representations generate amenable von Neumann 

algebras.) The subclass of approximately finite dimensional 

C*-algebras – AF C*-algebras – had been classified by Bratteli 

and Elliott. This work was perhaps one of the stimuli 

to the classification of amenable von Neumann algebras 

– these, it turned out, were exactly the von Neumann algebras 

generated by AF C*-algebras, and the invariant used 

to classify them, the Connes-Takesaki flow of weights, was 

notably an offshoot of Murray-von Neumann equivalence 

of projections – just like the invariant used in Elliott’s version 

of the AF algebra classification. Since AF algebras were 

just the first examples of amenable C*-algebras, much work 

still had to be done, but it was clear – once the possibility 

of a classification was realized – that K-theory – what the 

Murray-von Neumann comparison theory for projections 

had evolved into – would play an important role in this. For 

that matter, it had played an important role in the work of 

Jones. It had also been central to work of Brown, Douglas, 

and Fillmore, and of Kasparov, around the same time as the 

work of Bratteli and Elliott. Calculations of the K-groups 

of certain crossed product C*-algebras were made soon 

afterwards by Cuntz, by Pimsner and Voiculescu, and by 

Connes. This led to much else, with Connes discovering his 

8 

non-commutative Chern character based on cyclic cohomology, 

and subsequently, in collaboration with others, 

very important generalizations of the Atiyah-Singer index 

theorem. 

Around the same time that Jones and others were looking at 

(single) subalgebras of von Neumann algebras, Voiculescu 

was looking at freely independent families of subalgebras, 

in analogy with free groups, and, for almost the first time, 

obtaining conclusions concerning non-amenable von 

Neumann algebras. It was incidentally at about this time 

that Haagerup completed the missing case of Connes’s 

amenable von Neumann algebra classification, and that 

Elliott obtained the first classification result for (separable) 

amenable C*-algebras, beyond the case of AF algebras. 

(Other, similar, results followed.) In a spectacular triumph 

for the notion of amenability in operator algebras, soon 

after this, Popa, after much preliminary work by Ocneanu, 

arrived at a complete classification for amenable inclusions 

of von Neumann algebras (thus completing the program 

begun by Jones). 

One of the main areas of progress during the first Fields 

Institute program on operator algebras, during the twoyear 

period 1994 to 1996 (surrounding the move from 

Waterloo to Toronto!), was in the classification problem for 

amenable C*-algebras – by then sometimes referred to as 

the Elliott program. With the Kirchberg-Phillips classification 

of purely infinite simple C*-algebras obtained at that 

time, the classification program graduated from the consideration, 

albeit successful, of constructively defined special 

classes of algebras to the consideration of broad, axiomatically 

defined classes. The definitive result of Elliott, Gong, 

and Li on constructively defined algebras in the finite case, 

another of the main results obtained at that time, was some 

years later given an axiomatic formulation by H. Lin. Very 

recently, Zhuang Niu, a postdoctoral fellow in the program 

under review, together with Elliott, used Lin’s axiomatic 

method in a surprising way to obtain an isomorphism 

theorem for a larger class – for which the K-groups do not 

necessarily have the Riesz decomposition property. At the 

same time, the axiomatic method of Lin has been shown to 

be powerful in another way: certain algebras arising from 

dynamical systems, not known to belong to the class considered 

by Elliott, Gong, and Li, have been shown recently 

by Lin and Phillips to satisfy the axioms of Lin, and hence 

to belong to the (classifiable) class of Elliott, Gong, and Li. 

The Kirchberg-Phillips class of C*-algebras was characterized 

as the class of simple amenable C*-algebras absorbing 

as a tensor product factor the Cuntz algebra with K-group

the integers. During the present Fields program, considerable 

progress was made in characterizing in analogous 

terms the remaining simple amenable (separable) C*algebras 

which can be (expected to be) classified in terms 

of the invariants originally proposed by Elliott (namely, 

the ordered K-group together with traces). It should be 

mentioned that examples constructed by Villadsen (also 

during the first Fields program!), together with later work 

by Rordam and Toms, show that the Elliott classification 

program as originally proposed must be restricted to a 

subclass of the amenable C*-algebras, since in the general 

case new invariants will be needed – for instance, as Toms 

showed, the Cuntz semigroup. The conjectured characterization 

of the class suitable for (naive) classification is, 

simply, the simple amenable C*-algebras which absorb what 

has become known as the Jiang-Su algebra (also discovered 

during the first Fields program!). (This includes the 

Kirchberg-Phillips class, but excludes Rordam’s examples, 

which are infinite but not in the Kirchberg-Phillips class. 

As shown by Elliott and others, it includes examples which 

exhaust the values of the invariant, satisfying simple 

necessary conditions.) Considerable progress in this 

direction was made during the last year by participants in 

the Fields program, including Archey, Brown, Dadarlat, 

Elliott, Eilers, Gong, Jacob, Katsura, Kirchberg, Li, Lin, 

Niu, Perera, Phillips, Restorff, Rordam, Ruiz, Toms, Viola, 

and Winter. (In particular, it was shown by Winter that an 

enormous class of simple unital algebras, those for which 

the Kirchberg-Winter decomposition rank is finite, absorb 

the Jiang-Su algebra. This property is so general that it may 

even characterize those algebras which are finite and absorb 

the Jiang-Su algebra. The same conclusion for a much more 

concrete class, the class of simple inductive limits of matrix 

algebras over compact metric spaces with exponentially 

slow dimension growth, which overlaps, but, a priori, only 

partially, with Winter’s class – and of which there exist 

natural examples among those constructed by Villadsen 

– was obtained by Dadarlat, Phillips, and Toms; this class 

is contained in the class classified by Elliott, Gong, and Li, 

for which the above conclusion was established as a corollary 

of their classification, but the present direct approach 

is an enormous simplification.) Some progress, by several 

of those already mentioned and also Ciuperca, Coward, 

Ivanescu, Robert, and Santiago, was also made in the development 

of the Cuntz semigroup – introduced by Cuntz 

thirty years ago but never used as an invariant – as a tool 

for the purposes of classification. (In particular, Ciuperca 

and Elliott showed that the Cuntz semigroup, considered as 

an ordered semigroup, is a complete invariant for inductive 


limits of matrix algebras over the interval, including nonsimple 

ones.) 

The work of Uffe Haagerup, besides being fundamental 

for the theory of von Neumann algebras in general, and 

in particular supplying the final step in the classification 

of amenable von Neumann algebras (proving uniqueness 

in the one recalcitrant case that remained after Connes’s 

work), has contributed in major ways to three quite different 

areas of operator algebras that have begun relatively 

recently. The first of these is the theory of sub von Neumann 

algebras, or subfactors, begun by Jones, and finished 

in the amenable case by Ocneanu and Popa. The Haagerup 

subfactor, just one of Haagerup’s discoveries in this area, is 

a fiendishly difficult construction. The second new area is 

the theory of free probability, a merging of the theories of 

free groups and of large random matrices due to Voiculescu 

– studied by a strong group of mathematicians world-wide, 

including, in Canada alone, Belinschi, Collins, Mingo, 

Nica, and Speicher. In addition to contributing to free 

probability Haagerup discovered important applications of 

this new theory, on the one hand to the Elliott classification 

program, showing that the traces on an amenable 

unital C*-algebra map surjectively onto the states of the 

ordered K-group, and on the other hand to the invariant 

subspace problem, showing that almost every operator in 

a finite von Neumann algebra has an invariant subspace 

(this theorem was the subject of Haagerup’s Fields Institute 

Distinguished Lectures). The third new area in which 

Haagerup has contributed is the theory of operator spaces, 

begun by Effros and Ruan, and now studied world wide, 

and by a strong group in Canada including Choi, Davidson, 

Forrest, Lau, Kribs, Neufang, Runde, and Spronk. During 

the program Haagerup and Musat solved an important 

problem in the theory of operator spaces, the Effros-Ruan 

Conjecture. (More precisely, they solved the problem in the 

case of C*-algebras. The problem has a formidable history, 

including a solution for so-called exact operator spaces – in 

this case, the proof, due to Pisier and Shlyakhtenko – who 

like almost all mathematicians mentioned in this report 

were participants in the Fields program – uses Voiculescu’s 

free probability theory; not only did Pisier and Shlyakhtenko 

leave open the case of general operator spaces, and 

even general C*-algebras, but also their constant in the 

inequality conjectured by Effros and Ruan was not optimal; 

Haagerup and Musat not only considered arbitrary C*algebras 

but also obtained the optimal constant, which is 

one!) 

9


An interesting injection of set theory into operator algebras 

was provided during the program by a proof of Phillips 

and Weaver, on the one hand, that the Calkin algebra has 

outer automorphisms, and a proof by Farah, on the other 

hand – of course using different set theory axioms! – that 

every automorphism of this algebra is inner (the exact 

opposite statement). Farah also showed, with Katsura, that 

in the presence of suitable set theory axioms well-known 

questions of Dixmier concerning AF algebras could be 

settled. (In particular, an AF algebra, if not separable, can 

have K-group of rank one without being an infinite tensor 

product.) 

Two directions of work during the program were shown 

to be related in striking ways to the work of Jones. In work 

of Kawahigashi and Longo, certain ordered families of 

von Neumann algebras were classified, for the first time, 

and a particularly notable one was constructed with symmetry 

group the (Fischer-Griess) monster. In the course of 

this work, a connection (very intriguing – as a priori the 

two concepts might be thought to be entirely unrelated!) 

was discovered between the well known notions of Jones 

index and Fredholm index. In the work of Speicher and 

collaborators on non-crossing partitions, very important 

in the theory of free probability, certain diagrams used 

to represent these partitions were noticed to resemble 

diagrams used by Jones to represent his planar algebras, 

proposed by him recently as an alternative to the invariants 

of Ocneanu or Popa for subalgebras of von Neumann algebras. 

This resemblance was elucidated in work of Guionnet, 

Jones, and Shlyakhtenko, announced at one of the program 

workshops. (Their work consisted of a natural construction 

of an inclusion of von Neumann algebras corresponding to 

a given planar algebra. Very recently, a simplification of this 

construction was given by Kodiyalam and Sunder.) 

Important progress was achieved during the year in the 

program of Putnam and collaborators namely, Giordano, 

Skau, earlier, Herman, and, more recently, Matui), aiming 

to classify the orbit structure of an amenable equivalence 

relation on a Cantor set (assumed to have countable and 

dense orbits), in terms of the invariants of the corresponding 

C*-algebra. This very interesting program, a spin-off, 

perhaps, of C*-algebra classification theory but which very 

quickly took on a life of its own, had as a spectacular initial 

success the case of the equivalence relation corresponding 

to a single automorphism, but then took a long time to 

surmount the difficulties arising in connection even with 

the case of two commuting automorphisms. This year, the 

case of an arbitrary finite set of commuting automorphisms 

10 

(assumed to act freely and with dense orbits) yielded to 

intensive investigation. In an eerie echo of C*-algebra 

classification, in which wider classes of examples have 

frequently proved to coincide with a more modest, initial, 

class, the general finite commuting set of automorphisms 

turned out to give rise to the same orbit structure as a single 

automorphism. (And, analogously to the theorem of Dye 

and Krieger in the measurable case, the equivalence relation 

is the union of a sequence of finite relations, i.e., relations 

with equivalence classes of bounded finite order.) 

In conclusion, although in this brief space I have of course 

been unable to do justice to the work of the vast majority of 

the participants – if to that of any of them! – I believe that 

this year’s program on operator algebras can be seen to be 

a worthy successor to the earlier Fields Institute program 

thirteen years ago. One of its most noteworthy aspects, 

perhaps, and certainly one of the keys to its success, has 

been the readiness of participants from around the world, 

in effect, to help to finance the program – by systematically 

seeking support from all possible sources. 

If asked to comment on the effect of the program, I might 

however feel constrained to follow the lines of the reply 

reputedly given by Chou En-Lai to a similar question about 

the French Revolution: “It is perhaps too soon to tell.” 

George A. Elliott 

GRADUATE COURSES 

Functional Analysis 

Instructor: Andrew Toms 

Jul. 3-Aug. 30 2007 

This course provided students the basics required to profit 

from the Operator Algebra thematic program. It was York 

University’s graduate course, MA 6462, taught at the Fields 

Institute instead of at York. 

Introduction to Operator Algebras 

September 11–December 4, 2007 

Man-Duen Choi (Toronto), Ken Davidson (Waterloo) 

A course with this title could have many meanings. Man 

Duen Choi and Ken Davidson were asked by George Elliott 

to teach a course with this title, and decided to interpret 

this as a course in abstract operator algebras. Self-adjoint 

operator algebras (C*-algebras and von Neumann algebras) 

were abstractly characterized by Gelfand and Naimark (in 

1943) and by Sakai (in 1971). However, algebras without an 

adjoint operation which may be represented as algebras of

operators on a Hilbert space were not characterized until 

1990 by Blecher, Ruan, and Sinclair. One goal of this course 

was to get to a proof of this result. The course followed the 

very nice book of Paulsen, Completely bounded maps and 

operator algebras, and succeeded, with significant omissions, 

in covering much of the book, at least up to the end 

of the last chapter, including Paulsen’s proof of the BRS 

theorem using injective envelopes. Along the way, dilation 

theory and a variety of similarity problems were discussed. 

The course had good attendance of around fifty people for 

the whole time, including ten graduate students who took it 

as a credit course. Eight of the ten commuted from Waterloo. 

Including faculty and PDFs, there were about seventeen 

people on this commute, fourteen of whom were tough 

enough to take off at 7:45 a.m. in order to make the morning 

class as well. They had two vans with which to fight the 

rush hour traffic, and the drivers became expert at avoiding 

the Gardiner Expressway. They were significantly late only 

once. They envied, however, those able to move to Toronto 

for the term and avoid the commute. Many stayed on for 

the seminar and dinner before making the trek home. 

Ken Davidson 

Structure of C*-Algebras 

Instructors: George Elliott (Toronto), Chris Phillips 

(Oregon), Mikael Rørdam (Odense) 

Sep. 11 - Dec. 18 2007 

This regular working seminar was held as part of the 

Operator Algebras Thematic Program, allowing students 

an opportunity for intensive study of the structure of C* 

algebras. 

Free Probability 

September–December, 2008 

Instructors: Roland Speicher (Queen’s) and Jamie Mingo 

(Queen’s) 

Special lecture: Uffe Haagerup (University of Southern 

Denmark) 

In recent years a deep and important connection has been 

found between random matrices and free probability. The 

aim of this course was to present to novices in one or both 

of these two subjects an account of recent research connecting 

the two subjects. The audience consisted of graduate 

students and postdoctoral fellows from Queen’s University, 

University of Toronto, York University, and University of 

Waterloo. 


Random matrices have the object of much study in recent 

years by mathematicians, statisticians, physicists, and 

engineers. In statistics and engineering random matrices 

are used to analyze the large amounts of data arising from 

such diverse applications as genomics and wireless communication. 

Mathematicians are using random matrices as 

a calculating tool in combinatorics and algebraic geometry. 

In the study of random matrices one considers matrices 

whose entries are random and then studies the distribution 

of the eigenvalues of these matrices. A very simple way of 

studying the distributions of these eigenvalues is through 

their moments. When the size of the matrix is large, exact 

calculation of the moments is at best very complicated. 

However under certain circumstances, which occur quite 

often in applications, there is a method for getting approximate 

answers and the approximation gets better with the 

size of the matrix. This is the method of free probability. 

Free probability provides a universal rule for computing the 

moments of products of non-commuting random variables 

provided one knows the moments of individual random 

variables. This is done through an intriguing combination 

on complex analysis, operator theory, and combinatorics. 

The outline of the lectures was as follows. 

J. Mingo (September 13) 

Asymptotic freeness of independent Gaussian random 

matrices 

R. Speicher (September 27) 

Operator algebras and freeness 

R. Speicher (October 4) 

The free central limit theorem and free cumulants 

J. Mingo (October 11) 

Free harmonic analysis 

R. Speicher (October 18) 

Asymptotic freeness of random matrices 

J. Mingo (October 25) 

Applications to free group factors 

J. Mingo (November 8) 

Fluctuations of random matrices 

R. Speicher (November 22) 

Free entropy and large deviations 

11


Special guest lecture given by Uffe Haagerup (November 29) 

Brown’s spectral distribution measure for operators in a finite 

factor 

R. Speicher (December 6) 

Free entropy and operator algebras 

Notes and exercises from the course can be found at 

www.fields.utoronto.ca/programs/scientific/07-08/ 

operator_algebras/courses/index.html#free 

These notes will be soon published in book form in the 

Fields Institute Monograph series. 

Jamie Mingo 

WORKSHOPS 

Workshop on Noncommutative Dynamics and Applications 

July 16–20, 2007 

Organizers: William Arveson (Berkeley), B.V. Rajarama 

Bhat (Indian Statistical Institute), Remus Floricel (Regina), 

Robert Powers (Pennsylvania), Joachim Zacharias 

(Nottingham) 

Summer School in Operator Algebras 

August 13–24, 2007 

Held at the University of Ottawa 

Organizers: Thierry Giordano, Benoit Collins, David 

Handelman and Vladimir Pestov from the University of 

Ottawa. 

Workshop on Free Probability, Random Matrices, and Planar 

Algebras 

September 17–21, 2007 

Organizers: Jamie Mingo (Queen’s), Dietmar Bisch (Vanderbilt,) 

Roland Speicher (Queen’s), Alexander Soshnikov 

(Davis) 

Workshop on von Neumann Algebras 

October 29–November 2, 2007 

Organizers: Dietmar Bisch (Vanderbilt), Jamie Mingo 

(Queen’s), Narutaka Ozawa (Tokyo), Sorin Popa (UCLA), 

Dimitri Shlyakhtenko (UCLA), Roland Speicher (Queen’s), 

12 

Workshop on Structure of C*-Algebras 

November 12–16, 2007 

Organizers: Marius Dadarlat (Purdue), Eberhard Kirchberg 

(Humboldt), Huaxin Lin (Oregon), Ian Putnam (Victoria), 

Mikael Rørdam (Odense), Andrew Toms (York) 

Workshop on Operator Spaces and Quantum Groups 

December 11–15, 2007 

Organizers: Matthias Neufang (Carleton), Marius Junge 

(Illinois), Vern Paulsen (Houston), Gilles Pisier (Paris, 

Texas A&M), Zhong-Jin Ruan (Illinois 

The following, while not part of the formal thematic program 

on operator algebras, were very closely related to both 

the topic and participants of the program. 

Workshop on Around Connes’ Embedding Problem 

May 16–18, 2008 


36th Canadian Annual Symposium on Operator Algebras and 

Their Applications (COSy) 


Organizers: Man-Duen Choi (Toronto), George A. Elliott 

(Toronto), Raphael Ponge (Toronto), Andrew S. Toms (York) 

Noncommutative Geometry Workshop 


Organizers: Masoud Khalkhali (Western), Matilde Marcolli 

(Max Planck Institute, Bonn), and Guoliang Yu (Vanderbilt).

Workshop on Noncommutative Dynamics and 

Applications 

July 16–20, 2007 

Organizers: William Arveson (UC Berkeley), Remus 

Floricel (Regina), Robert Powers (Pennsylvania), Joachim 

Zacharias (Nottingham) 

As an important component part of the 2007 Thematic Program 

on Operator Algebras organized by Fields Institute, 

the Workshop on Noncommutative Dynamics and Applications 

brought together a strong group of mathematicians 

representing the current directions of development in the 

area. The main goals of this workshop were 

(i) to provide an opportunity for the participants to disseminate 

their results to a relevant audience 

(ii) to communicate recent developments in the various 

participating disciplines to experts in the same and in 

related areas 

(iii) to promote new and existing collaborations by giving 

an opportunity for participants to meet their colleagues 

in an intensive environment. 

The workshop achieved its goals by providing a forum 

of multidisciplinary interaction where a wide variety of 

research directions were represented, and results from different 

approaches were systematically compared. 

The themes and missions of the workshop, as well as the 

reputation of the Fields Institute allowed us to attract 

a large number of participants from all levels: graduate 

students, post-doctoral researchers, tenure-track professors, 

and senior scientists. There were 33 talks (either 25 or 55 

minutes long) given during the five days of this workshop. 

The audience comprised 110 participants from 13 different 

countries. 

Scientific Overview 

The workshop covered a variety of topics and methodologies 

in the theory of noncommutative dynamics: 

1. C* and W*-dynamical systems 

(i) C*-classification of classical dynamical systems 

(ii) symmetries and equilibrium in C*-dynamical 

systems 

(iii) C*-algebras from hyperbolic dynamical systems 

(iv) inclusion of C*-algebras 

(v) strongly self-absorbing C*-algebras 

(vi) crossed-products of C*-algebras by semigroups of 

endomorphisms 


(vii) topological quivers 

(viii) noncommutative Choquet boundaries 

(ix) means of unitary operators 

(x) operator algebras for multivariable dynamics 

2. Endomorphisms, Automorphisms and Completely Positive 

Maps of von Neumann and C*-algebras: 

(i) liftings of endomorphisms to automorphisms 

(ii) liftings of completely positive maps 

(iii) characteristic functions for contractive liftings 

3. E 0 -semigroups and Product Systems 

(i) classification of type II and type II product systems 

(ii) transitive product systems and gauge groups 

(iii) CP flows 

(iv) generalized CCR flows 

(v) dilations of E 0 -semigroups 

(vi) order and equivalence of E 0 -semigroups 

4. Quantum Dynamical Semigroups 

(i) dilations 

(ii) symmetric quantum dynamical semigroups 

(iii) Fredholm modules on Dirichlet spaces 

5. Quantum Probability and Quantum Information 

(i) quantum Markovianity 

(ii) quantum channels and capacity 

(iii) stochastic dilations 

(iv) distributional symmetries of exchangeabilityand 

contractibility 

(v) quantum error correction 

6. Noncommutative Dynamics in Free Probabilities 

(i) Free Meixner convolution semigroups 

7. Noncommutative Dynamics in Wavelet Theory 

(i) covariant representations associated to discrete 

dynamical systems 

(ii) random walks on branches 

(iii) iterated function systems 

8. Noncommutative Dynamics in Conformal Field Theory 

and Modular Invariants 

This broad range of topics made the workshop highly successful. 

The participants found themselves in an optimal 

environment where they could communicate their research 

ideas and interact with one another. 

13


Speakers: (in alphabetical order) 

Luigi Accardi (Università di Roma “Tor Vergata”) 

Quantum Markovianity: a survey 

Alexis Alevras (US Naval Academy) 

Order and equivalence of endomorphism semigroups 

Michael Anshelevich (Texas A&M) 

Free Meixner semigroups 

William Arveson (Berkeley) 

The noncommutative Choquet boundary 

Berndt Brenken (Calgary) 

Topological quivers as multiplicity free relations 

Nathaniel Brown (Penn State) 

Toward the C*-classification of classical dynamical systems 

Fabio Cipriani (Politecnico di Milano) 

Differential calculus and Fredholm modules on Dirichlet 

spaces 

Dennis Courtney (Berkeley) 

Lifting endomorphisms to automorphisms 

Santanu Dey (Ernst-Moritz-Arndt-Universität) 

Constrained liftings 

Kenneth Davidson (Waterloo) 

Operator algebras for multivariable dynamics 

Dorin Dutkay (Central Florida) 

Covariant representations in wavelet theory 

David Evans (Cardiff) 

Modular invariants 

Ruy Exel (Federal University of Santa Catarina, Brazil) 

A new look at the crossed-product of a C*-algebra by a semigroup 

of endomorphisms 

Rolf Gohm (Reading) 

Characteristic functions of liftings and applications to completely 

positive maps 

Ilan Hirshberg (Ben Gurion University of the Negev) 

Permanence properties of strongly self-absorbing C*-algebras 

Masaki Izumi (Kyoto) 

Type III factors distinguish type III E 0 -semigroups 

Palle Jorgensen (Iowa) 

Uses of operator algebraic methods in dynamics and in wavelet 

algorithms 

Richard Kadison (Pennsylvania) 

Means of unitary operators revisited 

14 

Claus Koestler (Carleton) 

On endomorphisms of von Neumann algebras from braid 

group representations 

Davide Kribs (Guelph) 

Some mathematical aspects of quantum error correction 

Marcelo Laca (Victoria) 

Symmetries and equilibrium in C*-dynamical systems 

Roberto Longo (Università di Roma “Tor Vergata”) 

Real Hilbert spaces, SL(2,R), modular theory and CFT 

Daniel Markiewicz (Technion) 

The gauge group of a strongly spatial E 0 -semigroup 

Hiroyuki Osaka (Ritsumeikan University) 

Inclusion of C*-algebras 

Robert Powers (Pennsylvania) 

Comparison theory for E 0 -semigroups 

Geoffrey Price (US Naval Academy) 

On some E 0 -semigroups induced from CP-flows 

Ian Putnam (Victoria) 

C*-algebras from hyperbolic dynamical systems 

Orr Shalit (Technion) 

E 0 -dilation of a pair of strongly commuting CP 0 -semigroups 

Kalyan Sinha (Indian Statistical Institute, Kolkata) 

Quantum dynamical semigroups and their stochastic dilations 

Michael Skeide (Università degli Studi del Molise) 

Products systems and quantum dynamics 

Baruch Solel (Technion) 

Operator algebras associated with unitary commutation relations 

Raman Srinivasan (Chennai Mathematical Institute, India) 

Generalized CCR flows 

Boris Tsirleson (Tel Aviv) 

Automorphisms of the type II Arveson system of Warren’s 

noise 

Remus Floricel 

Summer School in Operator Algebras 

August 13–24, 2007 


Organizers: Thierry Giordano, Benoit Collins, David 

Handelman and Vladimir Pestov from the University of 

Ottawa.

As part of the Fields Institute Thematic program in Operator 

Algebras, the University of Ottawa hosted a two-week 

Summer School in Operator Algebras August 13-24, 2007, 

sponsored by the Fields Institute 

The School was a great success. Over 55 mathematicians 

participated in it for at least one week and most of them 

attended both weeks. The participants came from Canada, 

the US and many European countries and several of them 

had already participated in the first Summer School organized 

in 2005. The success of the school is largely due to the 

exceptional quality of the lecturers, each of whom delivered 

a series of four 60 minute lectures and 2 problem sessions. 

The three sets of lectures in the first week were given by 

Dietmar Bisch (Vanderbilt), Narutaka Ozawa (Tokyo) and 

Matthias Neufang (Carleton). Dietmar gave an introduction 

to the theory of von Neumann subfactors. This theory 

essentially began with Vaughan Jones’ definition and study 

of the index of a subfactor N in a von Neumann factor M. 

Since the first work of Murray and von Neumann, the links 

between the theory of dynamical systems and operator 

algebras have always been deep and profound. The presence 

of a Cartan subalgebra in a finite continuous von Neumann 

factor M amounts to realizing M as a generalized version 

of the group measure space construction. In a recent series 

of remarkable works, S. Popa and N. Ozawa investigated 

the Cartan decomposition properties of classes of nonamenable 

type II 1 factors. Ozawa introduced these concepts 

and gave an overview of these recent results in his lectures. 

Operator space theory, first developed by Effros and Ruan, 

concerns closed subspaces of operators on a Hilbert space 

considered with the natural norm on matrices over the 

space. Neufang introduced the audience to the theory of 

operator spaces and their link with abstract harmonic 

analysis. 


In his lectures Vaes introduced the audience to discrete 

quantum groups and their probabilistic boundaries. 

The construction and the classification of crossed products 

are a central part the theory of both von Neumann and 

of C*-algebras. Phillips presented an introduction to the 

theory of crossed product C*-algebras, with emphasis on 

the background needed for recent work on the classification 

of crossed products. 

Speakers: 

Dietmar Bisch (Vanderbildt) 

Narutaka Ozawa (Tokyo) 

Matthias Neufang (Carleton) 

Jean Renault (Université d’Orléans) 

Stefaan Vaes (K.U. Leuven) 

N. Christopher Phillips (Oregon) 

Thierry Giordano 

Workshop on Free Probability, Random Matrices, and 

Planar Algebras 


Organizers: Dietmar Bisch (Vanderbilt), James Mingo 

(Queen’s), Alexander Soshnikov (UC Davis), Roland Speicher 

(Queen’s) 

The idea of this workshop, a part of the thematic program 

on Operator Algebras, was to bring together researchers 

working in free probability, random matrices, or planar 

algebras. Emphasis was on the use of diagrammatic methods, 

with the hope of revealing deeper connections between 

these fields, and of stimulating interaction and collaboration 

between these groups. There was a lot of interest in this 

In the second week, the three sets of lectures were given by 

Jean Renault (Orléans), Stefaan Vaes (K.U. Leuven) and 

N. Christopher Phillips (Oregon). In his lectures, Jean 

introduced the notion of a groupoid and the construction 

of the C*-algebra of a (topological) groupoid. Since the 

construction of the C*-algebra of foliations based on the 

holonomy groupoid, groupoids have played a very important 

role in noncommutative geometry. Quantum groups 

have had a broad impact in mathematics. In the compact 

case they were developed in the operator algebra setting by 

Woronowicz and very recently in the locally compact case 

by Kustermans and Vaes. Jamie Mingo and Chandler Davis 

15


workshop, which, with more than one hundred registered 

participants, was well attended. 

Over the last decade, the three topics of the workshop have 

been subjects of very active research with many surprising 

results. For example, impressive progress on the famous 

invariant subspace problem for operators on a Hilbert space 

has been made using the methods of free probability. In 

addition, planar algebras have been used to classify special 

classes of subfactors. Finally, the Tracy-Widom distribution 

has been isolated as a new universal distribution governing 

the fluctuations of many different random phenomena. 

For some time it has been suspected that there might exist 

deeper relations between these three a priori very different 

fields; the use of quite similar diagrammatic methods being 

one of the hints in this direction. One connection between 

free probability and random matrices (the asymptotic freeness 

of large classes of random matrices) was made precise 

by Dan Voiculescu, in 1991, and was instrumental in his 

spectacular result, a few years later, on the absence of Cartan 

subalgebras in the free group factors. Other relations of 

this kind continued to be more speculative–in particular, 

the connection between planar algebras and subfactors on 

one hand and random matrices and free probability on the 

other–but have since been confirmed. The workshop was 

the first of its kind to bring together the various groups and 

will further the deepening connection among these areas. 

The first three talks, given by the organizers, gave an 

introduction and survey of results and methods in the 

three fields. The following twenty-two talks were of a more 

specific nature, but as the audience had a quite varied 

expertise, each of them also provided some motivation and 

background for the problems considered. 

One highlight of the conference was the talk of Vaughan 

Jones about his joint work with Alice Guionnet and Dimitri 

Shlyakhtenko. In this work, they use ideas from random 

matrices for defining traces on planar algebras, which can 

then be utilized to construct subfactors. This sheds new 

light on a fundamental result in subfactor theory due to 

Sorin Popa and opens the way for a deeper understanding 

and many generalizations. 

The organizers received much positive feedback on the 

quality and accessibility of the talks. Ample time was left 

in the program for discussion among participants, and it 

was generally agreed that many new bridges were built linking 

the different groups and that new collaborations were 

begun. 

16 


Greg Anderson (Minnesota) 

Ubiquity of algebraic Stieltjes transforms 

Teodor Banica (Paul Sabatier University, Toulouse) 

Free probabilistic aspects of quantum algebra 

Dror Bar-Natan (Toronto) 

A very non-planar very planar algebra 

Dietmar Bisch (Vanderbilt) 

Subfactors and planar algebras 

Benoit Collins (Université Claude Bernard Lyon 1 and 

Ottawa) 

Weingarten calculus on enveloping algebras and non-commutative 

random matrices 

Valentin Feray (Université de Marne la Vallée Paris Est) 

Combinatorial description of Kerov’s character polynomials 

Pinhas Grossman (Vanderbilt) 

Intermediate subfactors 

Alice Guionnet (ENSL) 

Matrix models and map enumerations 

Ved Prakash Gupta (IMS) 

Planar algebra of the subgroup-subfactor 

Uffe Haagerup (University of Southern Denmark) 

Unbounded R-diagonal elements and applications to invariant 

subspaces 

Vaughan Jones (Berkeley) 

The graded algebras of a planar algebra 

Greg Kuperberg (Davis) 

Quantum central limit theorems 

Zeph Landau (The City College of New York) 

Quantum computation, the Jones polynomial, and tensor 

networks 

Roland Speicher/Jamie Mingo (Queen’s) 

Free probability and non-crossing partitions 

Alexandru Nica (Waterloo) 

Evolution towards boxplus-infinite divisibility in several 

variables 

Sandrine Péché (Grenoble) 

Universality results for the largest eigenvalue of sample covariance 

matrices 

Dima Shlyakhtenko (UCLA) 

Free stochastic calculus and its applications

Piotr Sniady (Wroclaw) 

Free probability and asymptotic representation theory of symmetric 

groups 

Alexander Soshnikov (UC Davis) 

Spectral properties of large random matrices with independent 

non-Gaussian entries 

Toufic Suidan (UC Santa Cruz) 

Fluctuations in the symmetric PNG process with a source 

Balint Virag (Toronto) 

Continuum limits of random matrices 

Dan Voiculescu (UC Berkeley) 

Aspects of free analysis 

Kevin Walker (Project Q, Microsoft, UCSB) 

TQFT completions of the annular Temperley-Lieb category 

Feng Xu (UC Riverside) 

On representing some lattices as lattices of intermediate subfactors 

of finite index 

Ofer Zeitouni (Minnesota) 

Consequences of ergodicity for some translation invariant 

determinantal processes and their approximations 

Jamie Mingo 

Von Neumann Algebras Workshop 

October 29–November 2, 2007 

Organizers: Dietmar Bisch (Vanderbilt), Jamie Mingo 

(Queen’s), Narutaka Ozawa (UCLA), Sorin Popa (UCLA), 

Dimitri Shlyakhtenko (UCLA) and Roland Speicher 

(Queen’s) 

Dietmar Bisch, Teodor Banica, Magdalena Musat and 

uffe haagerup 


This workshop was part of the thematic program on operator 

algebras, with an emphasis on subfactor theory, free 

probability and deformation/rigidity theory for II 1 factors 

in the sense of Popa. More than 100 participants attended 

the workshop including many students and postdoctoral 

researchers. 

The theory of subfactors gives rise to a very rich combinatorial 

structure that can be expressed in terms of operator 

algebras (as standard invariant, standard lattice in the 

sense of Popa), in categorical terms (as a certain C*-tensor 

category) or purely diagrammatically as a planar algebra, 

a notion due to Jones. Planar algebra techniques have led 

to recent rigidity results in subfactor theory – for instance 

the classification of quadrilaterals of subfactors with small 

indices. Asaeda reported on her recent proof showing that 

only the first two graphs in Haagerup’s infinite list of possible 

principal graphs for subfactors with indices below 5 

actually occur. Peters explained her construction of the 

Haagerup subfactor using planar algebra techniques. Several 

additional talks on subfactors and planar algebras were 

presented. Kawahigashi discussed a connection between the 

monster group and superconformal field theory via operator 

algebras. 

Popa’s deformation/rigidity techniques have led to the 

solution of several long-standing problems in the theory of 

II 1 factors. A number of talks were devoted to these recent 

breakthroughs, including a talk by Sorin Popa in which he 

gave a list of stimulating open problems. Ozawa presented 

a new result (joint with Popa) on the existence of II 1 factors 

with at most one Cartan subalgebra, and Vaes talked about 

a construction of II 1 factors whose fusion algebra can be 

computed completely. As an application he obtained the 

first examples of II 1 factors without non-trivial finite index 

subfactors. Several additional talks on related subjects such 

as cocycle superrigidity and von Neumman rigidity were 

presented by Ioana, Peterson and others. 

Connes’ embedding problem was the subject of a couple of 

talks. Shlyakhtenko discussed how to obtain lower bounds 

on free entropy dimension using free stochastic calculus, 

and Haagerup presented a solution of the Effros-Ruan conjecture 

for bilinear forms on C*-algebras (joint work with 

Musat). 

The workshop was very well received by the participants. 

The talks were very accessible, and a long lunch break and 

several additional shorter breaks during the program provided 

a lot of time for discussions, contributing greatly to 

the success of the workshop. 

17


Speakers: (as listed on program itinerary) 

Sorin Popa (UCLA) 

Some open problems on II 1 factors of group actions 

Narutaka Ozawa (UCLA) 

On a class of II 1 factors with at most one Cartan subalgebra 

Jesse Peterson (Berkeley) 

Group cocycles into the left regular representation and applications 

to II 1 factors 

Ken Dykema (Texas A&M) 

Horn’s inequalities and Connes’ embedding problem 

Nate Brown (Penn State) 

Embeddings into R w Ω 

Andreas Thom (Georg-August-Universität Göttingen) 

Group cocycles and affiliated operators 

Uffe Haagerup (Southern Denmark) 

Solution of the Effros-Ruan conjecture for bilinear forms on 

C*-algebras 

Stefaen Vaes (K.U.Leuven) 

Explicit computations of all finite index bimodules for a family 

of II 1 factors 

Adrian Ioana (Caltech) 

Cocycle superrigidity for profinite actions of Kazhdan groups 

Cyril Houdayer (UCLA) 

Another construction of type II 1 factors with a prescribed 

countable fundamental group 

Ionut Chifan (UCLA) 

(Title not available) 

Dan Shiber (UCLA) 

CCR random matrix models with potential 

Marta Asaeda (Riverside) 

Non-existense of finite depth subfactors with certain small 

indices 

Yasuyuki Kawahigashi (Tokyo) 

Superconformal field theory and operator algebras 

Dimitri Shlyakhtenko (UCLA) 

Algebras of q-semicircular elements and free stochastic calculus 

Kenley Jung (UCLA) 


Emily Peters (Berkeley) 

Constructing the Haagerup subfactor with planar algebras 

18 

Shamindra Ghosh (Vanderbilt) 

The planar algebra of the group-type subfactors of Bisch and 

Haagerup 

Roland Speicher (Queen’s) 


Hans Wenzl (San Diego) 

Subgroup type subfactors and twisted Kac-Moody algebras 

Mikael Pichot (Institut des Hautes Etudes Scientifiques) 

Intermediate rank and property RD 

Yoshimichi Ueda (Kyushu) 

Orbital free entropy and its dimension counterpart 

Remus Nicoara (Tennessee) 

Subfactors and Hadamard matrices 

Thierry Giordano (Ottawa) 


Magdalena Musat (Memphis) 

Classification of hyperfinite factors up to completely bounded 

isomorphism of their predual 

Claire Anantharaman-Delaroche (Université d’Orléans) 


Dietmar Bisch 

Workshop on the Structure of C*-algebras 

November 12–16, 2007 

Organizers: Marius Dadarlat (Purdue), Eberhard Kirchberg 

(Humboldt), Huaxin Lin (Oregon), Ian Putnam (Victoria), 

Mikael Rørdam (Odense), Andrew Toms (York) 

This workshop was organized in celebration of the sixtieth 

birthdays of Ola Bratteli (Oslo) and Akitaka Kishimoto 

(Kyoto). Speakers and participants came from Canada, 

China, Denmark, England, France, Germany, Israel, Japan, 

Norway, Puerto Rico, Scotland, Spain, and the United 

States. 

A C*-algebra is a subalgebra of the algebra of bounded 

linear operators on a Hilbert space which is closed in norm 

and under the formation of adjoints. The study of these 

objects was initiated by Frank Murray and John von Neumann 

in the 1930s, and it has grown to touch many areas of 

modern mathematics including geometry, number theory, 

and dynamics. This workshop concentrated on normseparable 

C*-algebras, which, in analogy with the classical 

Gel’fand-Naimark theorem, may be viewed as noncommutative 

topological spaces. Some of the major themes

were C*-algebras associated to groups and dynamics, G. A. 

Elliott’s program to classify separable amenable C*-algebras 

via K-theory, Kasparov’s K-theory and its variants, and the 

Cuntz semigroup. 

N. Christopher Phillips opened the conference with an 

account of some work in progress aimed at proving that 

the C*-algebras of minimal diffeomorphisms absorb the 

Jiang-Su algebra tensorially. His talk was connected to 

Wilhelm Winter’s later in the week, which presented an 

impressive classification theorem for C*-algebras absorbing 

the Jiang-Su algebra tensorially, and left the impression that 

the classification of A. Connes’ odd-sphere diffeomorphism 

algebras is imminent. George Elliott, the head of the thematic 

program’s Organising Committee, gave a stimulating 

lecture, Is Classification a chimera?, in which he proposed 

his classification functor formalism as a framework for 

unifying well-known classification results in the theory of 

operator algebras and beyond. 

Several talks revolved around the structure of the Cuntz 

semigroup and its applications. David Kerr presented recent 

work with Julien Giol which uses the Cuntz semigroup to 

prove that the C*-algebras of minimal dynamical systems 

need not be K-theoretically rigid, and exhibits an interesting 

connection between the mean topological dimension of 

a dynamical system and the comparison theory of positive 

elements in its associated C*-algebra. Mikael Rørdam spoke 

on joint work with Wilhelm Winter which provides several 

new characterisations of the Jiang-Su algebra, and gives a 

surprising criterion for embedding pieces of the Jiang-Su 

algebra in terms of the Cuntz semigroup. Leonel Robert 

described some properties of the Cuntz semigroup as a 

functor and a generalisation of Kasparov’s Stabilisation 

Theorem. 

The breadth of the applicability of K-theory was evident 

throughout the conference. Ralf Meyer described new tools 

and possibilities for computing the K-theory of non-simple 

C*-algebras, and Siegfried Echterhoff presented an overview 

of the theory and recent applications of K-fibrations. 

Marius Dadarlat demonstrated that the homotopy groups 

of the automorphism group of a Kirchberg algebra could 

be computed in terms of K-theory, and even gave a very 

accessible synopsis of the proof. Guihua Gong discussed the 

geometrization of the strong Novikov conjecture for residually 

finite groups, and last, but most certainly not least, 

Eberhard Kirchberg exposed several aspects of K-theoretic 

classification for strongly purely infinite non-simple C*algebras, 

with an emphasis on the role of regular Abelian 

subalgebras. 


The C*-algebras of dynamical systems and group actions 

made several appearances. In addition to David Kerr’s talk, 

we heard from Klaus Thomsen on applications of Elliott’s 

classification program to the C*-algebras of certain expansive 

dynamical systems, and from Takeshi Katsura on his 

joint work with N. Christopher Phillips on automorphisms 

of AF algebras with the Rohlin property. Hiroki Matui 

and Masaki Izumi gave classification theorems for actions 

on Kirchberg algebras and UHF algebras, and Huaxin Lin 

characterized embeddability into a simple AF algebra for 

crossed products of C(X) by Z d . Ilan Hirshberg presented 

his recent work on permutations of strongly self-absorbing 

C*-algebras. 

Of course, happily, not every talk is easily categorized! 

Soren Eiler’s talk revisited the semiprojectivity of mapping 

tori, while Nate Brown introduced new metric spaces 

associated to C*-algebras. Francesc Perera discussed the 

question of which Murray-von Neumann monoids could 

arise in graph C*-algebras, and Alex Kumjian introduced a 

method for producing new higher rank graph C*-algebras 

from old. Number theory and C*-algebras were joined in 

the talks of Florin Boca and Nadia Larsen, while Cornel 

Pasnicu presented work with Mikael Rørdam characterising 

real rank zero for purely infinite C*-algebras. MASAs in 

tensor products of non-nuclear C*-algebras were discussed 

by Simon Wassermann, and both Bruce Blackadar and Etienne 

Blanchard treated non-stable K-theory questions such 

as K 1 -injectivity and the structure of K-theory for unital 

free products. 

andrew Toms, ping wong ng, nate Brown, Jamie Mingo, 

ilan hershberg and Ken Dykema 

19



Florin Boca (UIUC) 

Continued fractions and operator algebras 

Bruce Blackadar (Nevada at Reno) 


Etienne Blanchard (Institut de Math de Jussieu) 

Proper infiniteness and K 1 injectivity (joint work with R. 

Rohde and M. Rordam) 


Metric space associated with tracial C*-algebras 

Marius Dadarlat (Purdue) 

The homotopy groups of the automorphism group of Kirchberg 

algebras 

Søren Eilers (Copenhagen) 

Semiprojectivity of non-commutative CW-complexes 

Siegfried Echterhoff (Münster) 

K-theoretic fibrations (based on joint work with Herve 

Oyono-Oyono and Ryszard Nest) 

George Elliott (Toronto) 

Is classification a chimera? 

Guihua Gong (Puerto Rico) 

Geometrization of strong Novikov conjecture for residually 

finite groups 

Ilan Hirshberg (Ben Gurion) 

Finite group actions on the Jiang-Su algebra 

Masaki Izumi (Kyoto) 

Classification Z2 actions on the Kirchberg algebras 

Chunlan Jiang (Hebei Normal) 

A complete classification of AI algebras and AC structure of 

AH algebras with ideal property 

Takeshi Katsura (Toronto) 

Generic automorphisms of approximately divisible AF algebras 

satisfy the Rohlin property 

David Kerr (Texas A&M) 

Dynamics and perforation 

Eberhard Kirchberg (Humboldt-Universität zu Berlin) 

Strong “UC” classes of non-simple C*-algebras 

Alex Kumjian (Nevada) 

k-morphs 

Nadia Larsen (Oslo) 

Hecke C*-algebras of semidirect products and KMS-states 

20 

Huaxin Lin (Oregon) 

Applications of the Elliott program 

Hiroki Matui (Chiba) 

Z2 – actions on UHF algebras 

Ralf Meyer (Göttingen) 

Computing Kirchberg’s bivariant K-theory 

Zhuang Niu (Calgary) 



Weak amenability of hyperbolic groups 

Cornel Pasnicu (Puerto Rico) 

Purely infinite C*-algebras of real rank zero 

Christopher Phillips (Oregon) 

Towards Z-stability of direct limits of recursive subhomogeneous 

C*-algebras 

Francesc Perera (Autonoma de Barcelona) 

Representing abstract semigroups as semigroups of projections 

of C*-algebras 

Leonel Robert (Fields Institute) 

Cuntz semi group of ideals and quotients and a generalized 

Kasparov stabilization theorem 

Mikael Rørdam (Southern Denmark) 

The Jiang-Su algebra revisited 

Klaus Thomsen (Aarhus) 

On the homoclinic and heteroclinic C*-algebras of expansive 

dynamical systems 

Andrew Toms (York) 

Topological vs. matricial dimension in C*-algebras 

Wilhelm Winter (Nottingham) 

Localizing the Elliott conjecture 

Simon Wassermann (Glasgow) 

MASAs, tensor products and the extension property 

Andrew Toms 

Workshop on Operator Spaces and Quantum Groups 

December 11–15, 2007 

Organizers: Marius Junge (Illinois), Matthias Neufang 

(Carleton), Vern Paulsen (Houston), Gilles Pisier (Paris and 

Texas A&M), Zhong-Jin Ruan (Illinois) 

The aim of this workshop – one of five within the framework 

of the thematic program on Operator Algebras – was

to bring together researchers working in two very active 

areas of modern functional analysis which both have their 

roots in operator algebra theory: the theory of operator 

spaces and completely bounded maps, on the one hand, 

and the theory of locally compact quantum groups, on the 

other hand. 

The closed self-adjoint subalgebras of the algebra B(H) 

consisting of all bounded operators on a Hilbert space H 

can be characterized abstractly via an intrinsic property of 

the algebra; these (abstract) algebras are called C*-algebras. 

Any such algebra A inherits naturally the structure of B(H) 

at each matrix level M n (A) ⊆ B(H n ). A corresponding 

characterization for closed subspaces of B (H) was given by 

Z.-J. Ruan (1988) through the formulation of two appropriate 

conditions on the norms of M n (X) for a Banach space 

X. The matricially normed spaces satisfying these ‘axioms’ 

are called (abstract) operator spaces. In the category of 

operator spaces, the morphisms are operators which respect 

this matricial structure in a suitable fashion, called completely 

bounded maps. The richness of the theory stems in 

particular from the multitude of very different operator 

space structures that a given Banach space may have, and it 

thus builds an exciting bridge between Banach spaces and 

C*-algebras: operator spaces are heading for the C*-world 

while standing on the ground of Banach spaces. The theory, 

developed by D.P. Blecher, E.G. Effros, U. Haagerup, M. 

Junge, V.I. Paulsen, G. Pisier, Z.-J. Ruan, et al., has had considerable 

impact on the development of functional analysis 

in different ways. On the one hand, through the solution 

of longstanding open problems, such as G. Pisier’s solution 

(1997) to the Halmos problem in operator theory from 

1970, and, completing earlier work by Pisier-Shlyakhtenko, 

Haagerup-Musat’s solution to the Effros-Ruan conjecture 

from 1991 regarding a Grothendieck-type inequality for 

jointly completely bounded bilinear forms on C*-algebras; 

in fact, the latter, presented in M. Musat’s talk, was achieved 

during the thematic program (cf. G. Elliott’s corresponding 

article)! On the other hand, a major influence of operator 

space theory is due to its creation of a suitable framework of 

‘non-commutative functional analysis’, which has proven 

very fruitful for areas such as Banach algebra theory and 

abstract harmonic analysis. 

One of the most fundamental themes of the latter field has 

been the concept of Pontryagin-type duality, and the search 

for a category that comprises both group algebras, their 

dual objects as well as other ‘group-like’ structures arising 

in mathematical physics, such as S.L. Woronowicz’s famous 

SU q (2). In 2000, J. Kustermans and S. Vaes, building on 

earlier work by Baaj-Skandalis, Enock-Schwartz and Kac- 


Vainerman, presented a simple set of axioms that, as they 

showed, are powerful enough to yield the above, thereby 

defining locally compact quantum groups. These are of 

course neither groups nor locally compact – yet their name 

is well-deserved since they consist of Hopf-von Neumann 

algebras M (the co-multiplication replacing the group 

multiplication) admitting weights (the analogue of left and 

right Haar measure on a locally compact group) which are 

invariant under the canonical left and right action of the 

predual M * on the image of . This theory currently brings 

together operator algebraists, operator spacers, Banach 

algebraists, abstract harmonic analysts, and mathematical 

physicists – indeed, all those – certainly overlapping – 

groups were present(ing) at the meeting, and we saw a week 

of very lively discussions between them. To give a concrete 

example of such a multiple meeting point, we mention the 

construction – developed in collaborations of Z. Hu, M. 

Junge, M. Neufang and Z.-J. Ruan (2007) and presented at 

the meeting by Z. Hu – of certain quantum channels, of 

interest in quantum information theory, that arise from the 

representation of the algebra M * = L 1 (G) over a quantum 

group G as completely bounded maps on B(L 2 (G)), and 

whose completely bounded minimal entropy can be calculated, 

in the finite-dimensional setting, by using G. Pisier’s 

complex interpolation theory for operator spaces. Various 

natural open questions were discussed in this context during 

the workshop, e.g., concerning the structure of the fixed 

point set of these channels, which in turn leads to the concept 

of non-commutative Poisson boundaries, as presented 

in R. Tomatsu and S. Vaes’s talks. 

In summary: an extremely fruitful meeting, on the level of 

questions as well as answers, and many new bridges built to 

generate more of both. 


Uffe Haagerup (Southern Denmark) 

Classification of hyperfinite factors up to completely bounded 

isomorphisms of their preduals 

Tao Mei (UIUC) 

Noncommutative H^1 and BMO spaces 

Timur Oikhberg (Irvine) 

Representations of Banach algebras as algebras of completely 

bounded maps 

Magdalena Musat (Memphis) 

The Effros-Ruan conjecture for bilinear forms on C¤-algebras 

Georgios Eleftherakis (Athens) 

Morita type equivalences for dual operator algebras 

21


Leonid Vainerman (University of Caen) 

Twisting of locally compact quantum groups, Deformation of 

the Haar measure 

Volker Runde (Alberta) 

Reiter’s property (P 1 ) for locally compact quantum groups 

Brian Forrest (Waterloo) 

Operator spaces and ideals in the Fourier algebra 

Piotr Soltan (Warsaw) 

On the Heisenberg double 

Matthew Daws (Leeds) 

Quantum compactifications of the Fourier algebra 

Zhiguo Hu (Windsor) 

Multipliers and the second dual of a Banach algebra 

Christian LeMerdy (University of Franche-Comté) 

Dilations on noncommutative Lp-spaces 

Hun Hee Lee (Waterloo) 

Finite dimensional subspaces of noncommutative L p spaces 

Françoise Lust-Piquard (Universite de Cergy-Pontoise) 

Generalized Ornstein-Uhlenbeck semi-groups on stratified 

groups 

Javier Parcet (CSIC) 

Mixed-norm inequalities and a transference method 

Nico Spronk (Waterloo) 

Convolutions on compact groups and Fourier algebras of coset 

spaces 

Marius Junge (UIUC) 

Embedding problems for subspaces of Lp 

Stefaan Vaes (K.U.Leuven) 

Boundaries of discrete quantum groups 

Reiji Tomatsu (Tokyo) 

Poisson boundaries of random walks on duals of q-deformed 

classical compact Lie groups 

Monica Ilie (Lakehead) 

Extensions of Fourier algebra homomorphisms 

Gastón García (Ciudad Universitaria) 

Quantum subgroups of a simple quantum group at roots of 1 

Khye Loong Yew (Toronto) 


David Blecher (Houston) 

Operator space methods for operator algebras 

22 

Quanhua Xu (University of Franche-Comté) 

Completely 1-summing maps between some homogeneous 

Hilbertian operator spaces 

Malgorzata Konwerska (UIUC) 

Law of the Iterated Logarithm in noncommutative probability 

spaces 


On a class of II 1 factors with at most one Cartan subalgebra 

Benoit Collins

New Trends in Harmonic Analysis Thematic Program January–June 2008 

Organizing Committee: Alex Iosevich (Missouri-Columbia), 

Izabella Laba (UBC) – lead organizer, Michael Lacey 

(Georgia Institute of Technology), Eric Sawyer (McMaster) 

Scientific Committee: Jean Bourgain (IAS), Michael Christ 

(Berkeley), John Friedlander (Toronto), W. Timothy Gowers 

(Cambridge), Andrew Granville (Montréal), Ben Green 

(Bristol), Bryna Kra (Northwestern) Kristian Seip (NTNU), 

József Solymosi (UBC), Elias Stein (Princeton), Terence Tao 

(UCLA) 

The Fields Institute thematic program New Trends in Harmonic 

Analysis took place from January 6 to June 30, 2008. 

The program had over 200 registered participants (shortterm 

and long-term). There were about 30 long-term 

visitors who participated for about 1 month or longer. This 

number included the 4 program organizers (all were in residence 

for most of the program), 8 other senior visitors, 11 

postdoctoral fellows and 8 graduate students. Other participants 

included short-term visitors (typically staying for 1- 2 

weeks) and various local faculty and students. Among the 

participants were three Fields Medallists (Jean Bourgain, 

Timothy Gowers, Terence Tao) and many other winners 

of major awards (Ben Green – Clay Research Award, Ron 

Graham and Endre Szemeredi – AMS Steele Prize, Michael 

Lacey, Christoph Thiele, Sergei Treil, Akshay Venkatesh, 

Alexander Volberg and Trevor Wooley – Salem Prize). 

The main organized activities were as follows: 

• Workshop on Recent Advances in Operator Theory 

and Function Theory, January 7-11, 2008, organized by 

Michael Lacey (Georgia Tech), Eric Sawyer (McMaster), 

Kristian Seip (NTNU). 

• Workshop on Harmonic Analysis, February 19–23, 2008, 

organized by Alex Iosevich (Missouri-Columbia), Malabika 

Pramanik (UBC). 

• Clay-Fields Conference on Additive Combinatorics, 

Number Theory, and Harmonic Analysis, April 5-13, 

2008, organized by Izabella Laba (UBC), David Ellwood 

(CMI), Andrew Granville (Montreal), Bryna Kra (Northwestern), 

Trevor Wooley (Michigan). The conference was 

co-sponsored by the Clay Mathematics Institute. 

• Distinguished Lecture Series: Timothy Gowers (Cambridge), 

Quadratic Fourier Analysis, April 9-11, 2008 

• Coxeter Lecture Series: Jill Pipher (Brown), Multi-Parameter 

Fourier Analysis, February 25-27, 2008 

izabella laba 


• Graduate course on Function and Operator Theory, Eric 

Sawyer (McMaster) 

• Graduate course on Analytic Number Theory, John 

Friedlander (Toronto) 

These activities have been reported on separately. Additionally, 

a research seminar was typically held 1-2 times per 

week from January to April whenever there was no conflict 

with other program events. The participants, especially the 

long-term visitors, have also reported that they very much 

appreciated the “quiet time” between the program events 

that provided the opportunity for collaboration and discussions. 

This has already resulted in a number of preprints 

and projects in progress. 

The major themes of the program include those listed 

below (with several key participants indicated). It should be 

understood that there is a significant amount of interaction 

and overlap between these areas, and that many other questions 

were also covered (to a lesser extent) by the program. 

• Kakeya, restriction and x-ray estimates, and related problems 

(Erdogan, Laba, Lacey, Muller, Oberlin, Pramanik, 

Seeger) 

• Harmonic-analytic methods in geometric measure theory 

(Iosevich, Laba, N. Lev, Mattila, Pramanik, Schul, Volberg) 

23


• Operator theory and function spaces (Davidson, Hytonen, 

Lacey, Pipher, Potts, Rochberg, Sawyer, Treil, Wick) 

• Harmonic-analytic methods in partial differential equations 

(Colliander, Erdogan, Goldberg, Ionescu, Pipher, 

Rogers, Smith, Vargas) 

• Bilinear and multilinear operators (Demeter, Grafakos, 

Lacey, X. Li, Muscalu, Thiele) 

• Fourier multipliers and Fourier integral operators 

(Greenleaf, Iosevich, Müller, Pramanik, Seeger) 

• Sum-product estimates in additive combinatorics (Bourgain, 

Glibichuk, Helfgott, Iosevich, Katz, Solymosi, Tao) 

• Szemeredi’s theorem, Green-Tao theorem, and related 

topics (Austin, Bergelson, Gowers, Green, Host, Kra, Tao, 

Samorodnitsky, Szemeredi, Ziegler) 

• Analytic and additive number theory (Balog, Bourgain, 

Bukh, Cojocaru, Croot, Friedlander, Granville, Green, V. 

Lev, Sanders, Tao, Wooley) 

Participants have expressed a high level of satisfaction with 

the organization and scientific content of the program. 

The junior personnel (graduate students and postdoctoral 

fellows) have particularly benefitted from the long-term 

exposure to a wide range of current research. We expect 

that the research conducted or initiated at Fields, and the 

connections and collaborations resulting from program 

activities, will have a significant long-term impact on the 

development of the field. 

We are grateful to the Fields Institute, its directorate and 

staff, for this opportunity and for all their encouragement, 

help and support. 

Izabella Laba 

GRADUATE COURSES 

Analytic Number Theory 

January–March 2008 

This course ran for 3 – 4 hours per week, attended by 

an average of 20 to 30 people comprising participants in 

the thematic program, graduate students, fourth year 

undergraduates and a few others. It was cross-listed as a 

University of Toronto Mathematics graduate course MAT 

1202 and as Department of Mathematics undergraduate 

course MAT 417. The goal was the provision of training 

in analytic number theory, especially as related to the 

distribution of primes, both for potential number theory 

students and for researchers in related areas of harmonic 

analysis. A particular aspect of this goal was the preparation 

of the audience as fully as possible for participation in 

the April workshop on Additive Combinatorics. 

24 

Topics: A selection of topics from the intersection of harmonic 

analysis and analytic number theory. Specifically: 

1. Introduction to statements of some of the famous problems 

and results of prime number theory. 

2. A little elementary background from number theory, 

algebra and complex analysis 

Complete proofs of the following were given: 

3. Dirichlet characters and L-functions and Dirichlet’s 

theorem on primes in arithmetic progressions. 

4. Prime Number Theorem with zeta-function theory 

needed for classical de la Vallée Poussin error bound. 

5. Prime Number Theorem for Arithmetic Progressions, 

Siegel’s theorem and Siegel-Walfisz theorem. 

6. Introduction to Hardy-Littlewood-Vinogradov method 

and its application to problems on primes. In particular, 

Vinogradov’s ternary Goldbach theorem and van der 

Corput-Chowla theorem on counting three term progressions 

of primes. 

7. Roth’s theorem on three term arithmetic progressions in 

sets of positive upper density. 

Also the main ideas behind the following were sketched, 

without detailed proof: 

8. Uniform distribution, Weyl’s criterion, estimation of 

exponential sums and theorem on uniform distribution 

of polynomial values. 

9. Further zeta and L-function theory and application to 

Hoheisel’s theorem on primes in short intervals. 

John Friedlander 

Function and Operator Theory 

Eric Sawyer 

During the January-June 2008 term, the Fields Institute 

held a Thematic Program on New Trends in Harmonic 

Analysis. One of the greatest benefits of the program was 

the interaction among the participants, greatly facilitated 

by the advanced graduate courses that gave interested 

students, post-doctoral researchers and participants in 

the program the opportunity to learn more about current 

research in harmonic analysis and related areas. One such 

class was Function and Operator Theory taught by Eric T. 

Sawyer, the McKay Professor of Mathematics at McMaster 

University. 

Roughly speaking, operator theory is the study of linear 

maps on a Hilbert or Banach space. One studies certain 

properties of the operator such as boundedness and

compactness. There is a strong connection between 

operator theory and complex analysis, especially complex 

function theory. In function theory, one has a space of 

functions that is governed by a norm as well as by other 

properties. One of the main goals of this course was to show 

how these two areas of mathematics interact. 

In function theoretic operator theory, there is typically an 

operator that is associated to a function in some canonical 

manner, with the hope that the behavior of the operator is 

directly related to some information about this function, 

such as the norm of the function in an appropriate space 

controlling the norm of the operator. One then seeks to play 

these two areas against each other, using the operator theory 

to deduce new function theoretic results, or using the 

function theory to determine the behaviour of the operator. 

Tools from harmonic analysis play a decisive role in this 

approach to studying these two areas of mathematics. 

The main topics covered in the lectures included: 

1. Interpolating sequences for classical function spaces and 

their multiplier spaces originating with Carleson’s characterization 

for Hardy space and its multiplier algebra of 

all bounded analytic functions. These ideas were further 

carried over into the setting of the Dirichlet space on the 

disc and the unit ball in several complex variables. 

2. Corona problems for classical function algebras starting 

with Carleson’s Corona Theorem for the bounded 

analytic functions on the disc and then continued to 

the analogous problem for the multiplier algebra for the 

Dirichlet space. 

3. The final topic was an introduction to the theory of 

Toeplitz and Hankel operators. This was connected to 

function theory via Fefferman’s Duality Theorem, and 

the problem of best approximation by analytic functions 

in the uniform norm. These topics connected with 

Hilbert space methods in analytic function theory, the 

Nevanlinna-Pick property and Commutant Lifting 

Theorems. 

These three main threads were interwoven in the lectures 

and presented so that students could gain a further understanding 

in a set of detailed lecture notes. 

The course served as an excellent introduction to this active 

area of analysis. Sawyer quickly introduced the students 

to the classical concepts and tools used and then brought 

them to the edge of modern research in this area. 

Brett Wick 

WORKSHOPS 


Workshop on Recent Advances in Operator Theory and 

Function Theory 

January 7–11 2008 

Held at the Fields Institute 

Organizers: Michael Lacey (Georgia Tech), Eric Sawyer 

(McMaster), Kristian Seip (NTNU) 


Sergei Treil (Brown) 


Alexander Volberg (Michigan) 

Uniqueness Theorem for Cauchy Potential 

Tavan Trent (Alabama) 

An algorithm for corona solutions (with bounds) for H ∞ 

Tao Mei (Texas A&M) 

Tent Spaces associated with semigroup of operators 

Artur Nicolau (Barcelona) 

Approximation by Interpolating Blaschke Products 

Richard Rochberg (WUSTL) 

Capacity, Carleson Measures, and Boundary Behavior 

Tuomas Hytonen (Helsinki) 

Kato’s square root problem in Banach spaces 

Dechao Zheng (Vanderbilt) 

Beurling type theorem on the Bergman space via the Hardy 

space of the bidisk 

Alexander Borichev (Bordeaux) 

Uniqueness theorems for (sub)harmonic functions 

Ken Davidson (Waterloo) 

A constrained Nevanlinna-Pick Interpolation problem 

Nir Lev (Tel-Aviv) 

Span of translates in L p (R), and zeros of Fourier transform 

Lingling Fan (Memorial) 

Strongly clean property and stable range one of rings 

Ignacio Uriarte-Tuero (Missouri) 

Removability problems for bounded, BMO and Hölder quasiregular 

mappings 

Michael Jury (Florida) 


Kasso Okoudjou (Maryland) 

Local well-posedness of nonlinear dispersive equations on 

modulation spaces 

25


Xuan Duong (Macquarie) 

Boundedness of Riesz transforms of magnetic Schrödinger 

Operators 

Mohammed Ali (Memorial) 


Harmonic Analysis Conference 

February 9–13, 2008 

Organizers: Alex Iosevich (Missouri-Columbia), Malabika 

Pramanik (UBC) 

The Harmonic Analysis conference at Fields Institute on 

featured a varied and exciting collection of speakers illustrating 

the diverse nature of modern harmonic analysis. 

Vitaly Bergelson discussed ten open problems on positive 

definite functions motivated by the application of ergodic 

theory to combinatorics. These exciting connections, pioneered 

by Furstenberg in late 70s and 80s, have motivated 

much recent work in harmonic analysis, ergodic theory and 

arithmetic combinatorics, including Green and Tao’s proof 

of the fact that subsets of the primes of positive density 

contain arbitrarily long arithmetic progressions. The topic 

introduced by Bergelson was continued nicely by Akos 

Magyar and Neil Lyall who brought a more pronounced 

number theoretic element into the discussion. The theme of 

arithmetic progressions was also represented in a lecture of 

Izabella Laba, who presented a beautiful result she proved 

with Malabika Pramanik on arithmetic progressions of 

length three in Salem subsets of the real line of Hausdorff 

dimension greater than 2/3. The discrete aspects of arithmetic 

problems were covered in a variety of contexts by 

Nets Katz and Derrick Hart who discussed various aspects 

of the sum-product in finite fields. 

The interaction of harmonic analysis and partial differential 

equations was represented in a series of excellent 

lectures by Alexandru Ionescu, Burak Erdogan, Michael 

Godlberg, Jim Colliander, Vladimir Mazya, Camil Muscalu, 

Jill Pipher, Eric Sawyer, Hart Smith, Ana Vargas 

and Xiangjin Xu, representing a considerable amount of 

diversity. Jim Colliander described a weakly turbulent 

solution of the cubic nonlinear Schrödinger equation on 

the two dimensional torus, a joint work with M. Keel, G. 

Staffilani, H. Takaoka and T. Tao. At the opposite end of 

the spectrum, Vladimir Mazya talked about boundedness 

of derivatives of order m -1 of solutions to the Dirichlet 

problem for the m-harmonic equation in an arbitrary 

3-dimensional domain, a joint work with Svetlana Mayboroda. 

26 

This conference has witnessed several very exciting developments 

in the field of multilinear operators. Christoph 

Thiele, Ciprian Demeter, Xiaochun Lie, Loukas Grafakos 

and Rodolfo Torres gave interesting and informative talks. 

Ciprian Demeter presented a joint result with Christoph 

Thiele on the two-dimensional bilinear Hilbert transform, 

an amazing breakthrough. Xiaochun Lie presented a proof of 

non-trivial bounds for the bilinear Hilbert transform along 

curves, an argument that combines in a very nice way the 

time-frequency analysis and the method of stationary phase. 

Classical harmonic analysis was also well represented in lectures 

by Andreas Seeger, Allan Greenleaf, Michael Bateman, 

Detlef Muller, Alex Nagel, Richard Oberlin, Raanan Schul, 

Alex Volberg, Sushrut Gautam, Alex Stokolos, Michael 

Lacey, Carlos Perez and Keith Rogers. Andreas Seeger 

presented joint work with Fedja Nazarov that constitutes 

major progress on the local smoothing conjecture of Sogge. 

Michael Lacey gave an insightful talk on the small ball 

inequality and its application to irregularity of distribution 

with respect to boxes, a problem that has been stalled since 

the fundamental work of Beck more than thirty years ago. 

Alexander Volberg gave a lecture on joint work with Eiderman 

and Nazarov on the electrostatic potential of finitely 

many charges, a classical problem to which they bring farreaching 

insight. 

In addition to excellent talks by senior mathematicians, 

this conference featured several first rate talks by young up 

and coming mathematicians like Michael Bateman, Derrick 

Hart, Doowon Koh and Lilian Pierce. Michael Bateman 

energized the audience with his proof of the L p estimates 

for a maximal operator along rectangles pointed in the 

direction of a vector field in R 2 depending on one variable, 

following up in a deep and interesting way on recent work 

by Lacey and Lie. 

The conference exceeded all expectations by bringing 

together experts from a broad range of areas of mathematics 

where harmonic analysis has played a decisive role. The 

connections between these areas are still expanding and 

will continue to develop in the foreseeable future. 


Christoph Thiele (UCLA) 

A modulation invariant bilinear variant of the T(1) theorem 

Cirprian Demeter (IAS and University of Indiana) 

Bounds for the two dimensional bilinear Hilbert transform 

Xiaochun Li (UIUC) 

Some problems on bilinear oscillatory integrals along curves

Alexander Stokolos (DePaul University) 

On the Tauberian condition for geometric maximal operators 

Sushrut Gautam (UCLA) 

A critical-exponent Balian-Low theorem 

Rodolfo Torres (Kansas) 

New maximal functions and commutator and weighted estimates 

for the multilinear Calderón-Zygmund theory 

Loukas Grafakos (University of Missouri at Columbia) 

Rough and rougher singular integrals 

Richard Oberlin (UCLA) 

Some estimates for the X-ray transform 

Vitaly Bergelson (University) 

10 open problems on positive definite functions 

Neil Lyall (University of Georgia, Athens) 

Polynomial configurations in difference sets 

Akos Magyar (University of Georgia, Athens) 

A coloring problem for squares 

Lillian Pierce (Princeton) 

Discrete fractional integral operators 

Derrick Hart (University of Missouri-Columbia) 

Sum-Product theory in finite fields 

Doowon Koh (University of Missouri-Columbia) 

Extension theorems for paraboloids in the finite field setting 

Alexander Nagel (University of Wisconsin, Madison) 

A covering lemma for certain monomial polyhedra 

Michael Lacey (Georgia Tech) 

The small ball inequality in all dimensions 

Raanan Schul (UCLA) 

Towards uniform rectifiability in a general metric space 

Alexandru Ionescu (Madison) 

Semilinear Schrodinger flows on hyperbolic spaces: scattering in H 1 

Keith Rogers (Universidad Autonoma de Madrid) 

Mixed-norm estimates for the free Schrodinger equation 

Burak Erdogan (UIUC) 

Near-linear evolution for 1D periodic NLS 

Michael Goldberg (Johns Hopkins) 

Strichartz estimates in the presence of an oscillating electromagnetic 

field 


Alexander Volberg (Michigan State University, East Lansing) 

Electrostatic field with finitely many charges: the sharp estimates 

of the size of the level sets 

Hart Smith (Washington) 

L p bounds for eigenfunctions for Lipschitz metrics 

Allan Greenleaf (Rochester) 

Estimates for Fourier integral operators with both singular 

symbols and folds 

Carlos Perez (Seville) 

Sharp weighted end-point estimates for Calderon-Zygmund 

Singular Integral Operators 

Steve Hofmann (University of Missouri, Columbia) 

Layer potentials for complex divergence form equations 

Jill Pipher (Brown) 

Some remarks on absolute continuity of elliptic measure 

Vladimir Mazya (Ohio State) 

Higher order elliptic equations in general domains 

Xiangjin Xu (Binghamton) 

Upper and lower bounds for normal derivatives of spectral 

clusters of Dirichlet Laplacian 

Andreas Seeger (Madison) 

Radial Fourier multipliers and a local smoothing inequality 

Camil Muscalu (Cornell) 

On an interesting multi-parameter structure in harmonic 

analysis and its connection to the theory of differential equations 

Ana Vargas (Universidad Autónoma de Madrid) 

Null form estimates for the wave equation 

Michael Bateman (Indiana University-Bloomington) 

Maximal averages along one-variable vector fields 

Detlef Muller (Christian-Albrechts-Universitt zu Kiel) 

Sharp L p -estimates for maximal operators for p > 2 , oscillation 

indices and a Fourier restriction theorem associated to 

hypersurfaces in R 3 

Izabella Laba (UBC) 

Arithmetic progressions in sets of fractional dimension 

Jim Colliander (Toronto) 

Weak turbulence for cubic NLS on the two dimensional torus 

Nets Katz (Indiana, Bloomington) 

Sums, Products, and other things 

Eric Sawyer (McMaster) 

Nehari theorems for the Dirichlet space 

Alex Iosevich 

27


The Clay-Fields Conference on Additive Combinatorics, 

Number Theory and Harmonic Analysis 

April 5–13, 2008 

Organized by David Ellwood (CMI), Andrew Granville 

(Montreal), Bryna Kra (Northwestern), Izabella Łaba 

(UBC; committee chair) and Trevor Wooley (Bristol) 

This conference, co-sponsored by the Clay Mathematics 

Institute, was the largest event of the Winter-Spring 2008 

Harmonic Analysis thematic program, and was a major 

event in the field, probably the largest in the last 2 years. 

It featured over 40 speakers, including most of the leaders 

in the area, junior researchers, and leading scientists 

in related fields whose work has connections to additive 

combinatorics. We were particularly honoured to host three 

Fields medalists: Jean Bourgain (IAS), Timothy Gowers 

(Cambridge) and Terence Tao (UCLA), as well as Endré 

Szemerédi, who had just been awarded the Steele prize 

for his 1974 proof of what is now known as Szemerédi’s 

theorem. The Distinguished Lecture Series given by Tim 

Gowers (April 7-9) was a major highlight of the conference. 

The meeting was very well attended, both by senior mathematicians 

and by students and junior scientists. For the 

beginners, it was an excellent way to be introduced to the 

subject; the experts had an opportunity to catch up on 

recent developments, and engage in discussions and collaboration. 

Additive combinatorics is an emerging area of mathematics 

that combines elements of number theory, combinatorics, 

harmonic analysis and ergodic theory. Its best known 

results include Szemerédi’s theorem on arithmetic progressions 

in dense sets of integers, the Green-Tao theorem on 

arithmetic progressions in the primes, sum-product estimates, 

the Freiman-Ruzsa theorem on the structure of sets 

with small sumsets, and much more. The problems under 

consideration can often be stated in terms of grade-school 

arithmetic, while solutions can range from surprisingly 

simple to deep and highly sophisticated. 

Szemerédi’s theorem states that if a set A⊂ Z contains 

a positive proportion of the integers, it must contain a 

k-term arithmetic progression for any k. At this point, it 

has several substantially different proofs: combinatorial 

via regularity lemma (due to Szemerédi), ergodic-theoretic 

(Furstenberg), harmonic-analytic (Gowers), combinatorial 

via hypergraph theory (Gowers and, independently, 

Nagle-Rödl-Schacht-Skokan). Each of them was a major 

milestone in combinatorics, introducing new methods and 

28 

opening new directions of research: for example, Furstenberg’s 

ergodic-theoretic approach led to several far-reaching 

generalizations such as the multidimensional Szemerédi 

theorem and the density Hales-Jewett theorem (both due 

to Furstenberg-Katznelson), or the polynomial Szemerédi 

theorem (Bergelson-Leibman). We are still quite far, however, 

from a complete understanding of the subject, and 

many questions remain open. 

The conference included a number of talks related to Szemerédi’s 

theorem and its extensions. Vitaly Bergelson and 

Nikos Frantzikinakis talked about their recent work (joint 

with Alexander Leibman and Randall McCutcheon, and 

with Maté Wierdl and Emmanuel Lesigne, respectively) 

on extensions of the Bergelson-Leibman theorem to new 

classes of functions that are not polynomial, but still have 

good enough equidistribution properties. Bernard Host 

lectured on his joint work with Bryna Kra on nilsequences 

and their applications in ergodic theory and additive combinatorics. 

The combinatorial approach was represented by 

Balázs Szegedy, who presented a “symmetric” variant of the 

regularity lemma and an application to additive number 

theory. Tim Austin discussed a quantitative version of the 

Furstenberg-Katznelson proof of the Hales-Jewett theorem. 

One of the best-known results in additive combinatorics 

is the proof by Ben Green and Terence Tao that the primes 

contain arbitrarily long arithmetic progressions. Subsequently, 

Green and Tao went on to develop a program 

aimed at a very general conjecture (due to Hardy-Littlewood 

and Dickson) on the asymptotic number of solutions 

to linear equations in the primes. The conjecture includes 

the Green-Tao theorem as a special case, corresponding 

to a system of k-1 equations x j+2 + x j = 2x j+1 in k variables 

x 1 ,…,x k , but it also makes the stronger claim that the number 

of such progressions in the primes less than N follows 

certain prescribed asymptotics. It also implies formally the 

Goldbach conjecture (every even number is a sum of two 

primes) and the twin primes conjecture (there are infinitely 

many pairs of primes p, p+2). The ultimate goal of the 

Green-Tao program is to prove the “non-degenerate” case 

of the Dickson conjecture. “Non-degenerate” means that 

the system of equations does not include or encode implicitly 

any equation in two variables; thus the success of the 

Green-Tao program would not resolve “binary” questions 

such as the Goldbach and twin primes conjectures, but it 

would yield precise asymptotics on the number of k-term 

arithmetic progressions in the primes for every k. 

About two years ago, Green and Tao reduced the problem 

to proving two conjectural statements: the inverse Gowers

norm conjecture and the Möbius-nilsequences conjecture. 

They also proved both statements to the extent needed to 

resolve the case of 2 equations in the primes. Independently 

and in a different context, Alex Samorodnitsky proved an 

analogous case of the inverse Gowers norm conjecture in 

fields of characteristic 2. 

In his two lectures at the conference, Terence Tao 

reported that he and Green have now proved the Möbiusnilsequences 

conjecture in its full generality; their proof 

combines number-theoretic methods (the “circle method”) 

and a new Ratner-type theorem for nilmanifolds. Ben Green 

gave an update on the inverse Gowers norm conjecture. Last 

year, Lovett-Meshulam-Samorodnitsky and (independently 

and about the same time) Green-Tao found finite field 

counterexamples to the most general form of the conjecture. 

However, Green and Tao have recently proved that this 

particular type of counterexample cannot occur in fields of 

sufficiently large characteristic; hence they continue to be 

optimistic that the conjecture will be true in Z N . 

Tamar Ziegler lectured on another major development 

inspired by the Green-Tao theorem: the proof, by Tao 

and Ziegler, of the polynomial Szemerédi theorem in the 

primes. Their work relies on the ergodic-theoretic methods 

of Furstenberg and Bergelson-Leibman, as well as a new 

variant of the “transference principle” of Green and Tao. 

The latter states, roughly speaking, that sets such as primes 

– which have asymptotic density zero, but are sufficiently 

randomly distributed – can be modelled by sets of positive 

asymptotic density. This allows us to transfer results known 

for sets of positive density, such as the Szemerédi and 

Bergelson-Leibman theorems, to the primes setting. 

Another very active area of research concerns the sum-product 

estimates. Let A be a set of real numbers. We will write 

A+A={a+a': a,a' ∈ A} and A·A= {aa' : a,a' ∈ A}. What can 

we say about the minimum size of A+A and A·A? It is easy to 

see that each set has cardinality at least 2|A| - 1 and that this 

lower bound is attained if A is an arithmetic or geometric 

progression, respectively. Nonetheless, Erdös and Szemerédi 

conjectured that at least one of A+A and A·A must be large. 

Just before this article was written, Jozsef Solymosi proved 

that min (|A+A|, |A·A|) ½ |A| 4/3 (log|A|) -1/3 , which is the 

best lower bound known 

so far. 

A few years ago, Bourgain-Katz-Tao first extended this type 

of estimate to the finite field setting. This was followed 

by a rush of activity, motivated by the applications that 

sum-product estimates have found in number theory, com- 


binatorics and computer science. Mei-Chu Chang, Alexei 

Glibichuk, Alex Iosevich and Chun-Yen Shen all spoke on 

sum-product estimates in finite fields, including variants 

for multiple sumsets and product sets and applications 

to exponential sum estimates and distance set problems. 

Harald Helfgott lectured on his “growth theorem” in SL 3 : if 

a set A ⊂ SL 3 (Z/pZ) is not “too large”, then |A*A*A| |A| 1+ . 

There were many other fascinating talks on combinatorics, 

additive and analytic number theory, given by Antal Balog, 

Ron Graham, Alex Gamburd, Andrew Granville, Vsevolod 

Lev, Maté Matolsci, Jaroslav Nesetril, Tom Sanders, Jozsef 

Solymosi, Endré Szemerédi, Trevor Wooley, and others. 

I would like to close by mentioning a few talks that featured 

connections between additive combinatorics and other 

areas of research. Jean Bourgain talked about a question 

in ergodic theory concerning the rigidity of invariant 

measures on 2-dimensional tori; the solution (joint work 

with Furman, Lindenstrauss and Mozes) features an 

application of sum-product estimates. Alex Samorodnitsky 

spoke on pseudorandomness and structure in “property 

testing” in theoretical computer science: this is the line of 

work that led him, independently of the Green-Tao work, 

to the Gowers inverse norm conjecture mentioned earlier 

in connection with Green’s talk. Akshay Venkatesh gave 

a “speculative” lecture about his joint work with Jordan 

Ellenberg on modelling number-theoretic phenomena by 

the statistics of seemingly unrelated random objects such as 

matrix groups. 


Andrew Granville (Montreal) 


Trevor Wooley (Bristol) 


Alexey Glibichuk (Moscow State) 

Additive properties of product sets in finite fields 

Philip Matchett Wood (Rutgers) 

Polynomial Frieman isomorphisms 

Ron Graham (San Diego) 

Some Ramsey results for the n-cube 

Alina Cojocaru (Illinois-Chicago) 

The Koblitz conjecture on average 

Vitaly Bergelson (Ohio State) 

Generalized polynomials and an extension of the polynomial 

Szemeredi Theorem 

29


Tamar Ziegler (Technion) 

Polynomial patterns in primes 

Yonutz Stanchescu (Open University of Israel) 

On the exact structure of multidimensional sets with small 

doubling property 

Boris Bukh (Princeton) 

Sums of dilates 

Van Vu (Rutgers) 


Yu-Ru Liu (Waterloo) 

Vinogradov’s mean value theorem in function fields 

Terry Tao (UCLA) 

The Mobius-Nilsequences conjecture 

Alex Samorodnitsky (Hebrew University) 

Low degree tests at large distances 

Ernie Croot (Georgia Tech) 

On rich lines in grids 

Antal Balog (Renyi Institute) 

Trigonometric sums with multiplicative coefficients 

Mate Matolsci (Renyi Institute) 


Alexander Gamburd (University of California, San Diego 


Kevin Costello (IAS) 


Akshay Venkatesh (Courant) 

Random permutations in number theory 

Vsevolod Lev (University of Haifa at Oranim) 

On the number of popular differences 

Gregory Freiman (Tel Aviv University) 

On a detailed structure of sumsets and difference sets 

Mei-Chu Chang (UC Riverside) 


Alex Iosevich (Missouri-Columbia) 

Distribution of dot products in vector spaces in finite fields 

and applications to problems in additive number theory and 

geometric combinatorics 

Chun-Yen Shen (Indiana) 

Quantitative sum-product estimates 

30 

Bernard Host (Marne-la-Vallee) 

Nilsequences in ergodic theory (joint work with B. Kra) 

Distinguished Lecture Series: Timothy Gowers (Cambridge) 

Quadratic Fourier Analysis 

Harald Helfgott (Bristol) 

Growth in SL3 Jean Bourgain (IAS) 

Invariant measures and stiffness for non Abelian actions on tori 

Tim Austin (UCLA) 

A very brief look at the Density Hales-Jewett Theorem 

Jaroslav Nesetril (Prague) 


Ben Green (Cambridge) 

Exponential sums and Gowers norms in finite field models 

Tom Sanders (IAS) 

Chowla’s cosine problem in abelian groups 

Matthew Smith (Georgia) 

On solution-free sets for simultaneous additive equations 

Jean Bourgain (IAS) 


Jozsef Solymosi (UBC) 


Balazs Szegedy (Toronto) 

The symmetry preserving regularity and removal lemmas 

Neil Lyall (Georgia) 

Optimal polynomial return times 

Mate Wierdl (Memphis) 

Bases of integers and Hardy fields 

Nikos Frantzikinakis (Memphis) 

Szemerédi’s theorem, Hardy sequences, and nilmanifolds 

Weidong Gao (Nankai) 

Zero-sum problems in Abelian Groups 

Mihalis Kolountzakis (University of Crete) 

The discrepancy of a needle on a checkerboard 

Endre Szemeredi (Rutgers) 


Izabella Laba

Lectures 

COxETER LECTURE SERIES 

Jill C. Pipher (Brown) 

Multiparameter Harmonic Analysis 

Feb. 26, 27 & 28, 2008 

A. Zygmund called the classical theory of Fourier analysis 

the ‘meeting ground of real and complex analysis.’ Already 

in the classical Fourier theory at the beginning of the last 

century we find the origins of modern mathematical ideas 

and applications to a variety of themes of great current 

interest. These include operator and complex function 

theory, potential theory and boundary value problems, 

well-posedness for linear and nonlinear pde’s, additive 

number theory and primes in arithmetic progressions, 

theta functions and L-series, decomposition of function 

spaces, signal analysis, singular integrals, and oscillatory 

integrals. 

Pipher’s lectures discussed a higher dimensional (or 

product theory) aspect of Fourier analysis. The defining 

characteristic of the set of questions associated with this 

theory concerns operations that exhibit a more general set 

of dilation invariance properties. It too has connections 

to both real and complex function theory, from analytic 

function theory of the bi-disc to the summation of multiple 

Fourier series, as well as regularity properties of harmonic 

functions on symmetric spaces. Some of the modern 

questions center on issues related to singular integrals, 

Hardy spaces, averaging, bilinear operators, and reach into 

Barbara Keyfitz, Jill pipher and Michael lacey 


probability theory through multi-parameter martingales, 

and higher dimensional Brownian sheets. 

The representation of a function as a sum of simpler 

(atomic) pieces, and the associated reconstruction and 

convergence issues, has been the fundamental theme in 

Fourier theory. There are various aspects of the classical 

theory which make it easier to constructively obtain such 

ecompositions. The classical theory in R d is a one-parameter 

theory, which essentially means that the extension 

to d dimensions of operators like the Hilbert transform 

on the line is based on invariance under a one parameter 

family of dilations. The function spaces which arise in 

connection with such operators may then be defined via 

decompositions involving cubes (or balls), giving us tools 

like maximality and stopping time arguments. By contrast, 

the product theory introduces natural operators and function 

spaces invariant under some k dimensional family of 

dilations in R d , a truly higher dimensional structure. 

Some estimates in the product theory are available by iteration. 

For instance, the simplest higher-parameter operator 

is the maximal function acting on functions on R d formed 

at point x ∈ R d by taking the supremum over all averages 

of f over rectangles that contain x. The class of rectangles 

is invariant under a full d-dimensional group of dilations, 

and is called the Strong Maximal Function. Its simplest L p 

properties are available by iteration of the one-dimensional 

maximal function. Finer endpoint properties of the 

maximal function are not available by this method. For 

this maximal function, these properties hinge upon covering 

lemmas. Covering lemmas assert decompositions of 

arbitrary collections of rectangles into two collections: the 

first is small in that the measure of its union is controlled 

by the union of the second, and the second collection has 

rectangles with bounded overlaps. In one parameter theory, 

the second collection consists of disjoint rectangles, which 

obviously have no overlap, but in higher parameter theory, 

bounded overlap has to be understood in terms of an exponential 

integrability condition. 

For the maximal function, this theory was developed by 

Cordoba and R. Fefferman. But a full development of this 

theory still awaits us. For instance, consider the maximal 

function acting on functions on R 3 obtained by forming a 

maximal function over rectangles with sidelengths given by 

s, t, (st), respectively. Here, is some reasonable increasing 

function, say a power. Thus, these rectangles exhibit a 

31


dilation invariance with respect to a two-parameter group 

of dilations. It was a key conjecture of Zygmund that such 

a maximal function should have the central characteristics 

of the Strong Maximal Function on R 2 . Antonio Cordoba 

verified this, utilizing a second central aspect of the subject: 

In the two-parameter case, one can ‘freeze’ one parameter, 

reducing to the (much easier) one-parameter case. Thus, 

two-parameter theory is more advanced and specialized 

that the general case. As a key illustration of this, consider 

the maximal function acting on functions in R 4 given 

by taking the maximal average over rectangles with sidelengths 

given by s,t,u, stu. The Zygmund conjecture is that 

this maximal function exhibits the central properties of the 

Strong Maximal Function on R 3 , and indeed this is a key 

open question in the subject. 

In other aspects, the iteration technique is simply not available. 

A key illustration of this fact is in the theory of BMO, 

the space of bounded mean oscillation, which plays a profound 

role in the one-parameter theory. To summarize this 

theory we will stay in the realm of the dyadic version of this 

space, which admits simpler description in this case. Let 

D = { [j2 k , (j +1)2 k ) : j, k ∈ Z} be the dyadic intervals on 

R, which are invariant with respect to the one-parameter 

group of dilations by a power of 2. BMO then has a simple 

intrinsic definition, which explains the name: 

Here fI =| I | 

 

−1 

∫ fdx is the mean value of f over I. Thus, f 

is in the space BMO I iff its oscillation from its mean admits 

a uniform control. Clearly, every bounded function satisfies 

this estimate, but this condition is more general as the 

unbounded ln x is in BMO. What is the higher-parameter 

version of BMO? It is straighforward to find a tensor 

product variant of the definition above, controlling the 

‘oscillation’ of f over a rectangle. Such spaces, attractive in 

their own right, are referred to as ‘rectangular BMO’ and 

denoted as BMOrec . They are not BMO, as fundamental 

examples of Lennart Carleson demonstrate. It was the 

striking work of Alice Chang and Robert Fefferman to 

characterize BMO, but in an extrinsic fashion. 

32 

sup 

I ∈D 

1 

| I | 

∫ 

I 

| f − f I | 2 dx

transform. The proof requires not only all the techniques 

associated with the multiparameter Hankel forms, but 

a suitable set of real-variable techniques to replace those 

specialized to the analytic setting. The Coifman- Rochberg- 

Weiss result has had a far-reaching impact in the areas of 

compensated compactness. This new result supplies multiparameter 

variants of such results. 

Multi-parameter analysis plays a role in Leibniz rules for 

differentiation. The simplest possible form of such a rule 

would be 

Thus, the derivative can be moved to either term. This 

indeed is true, and follows from the theory of pseudodifferential 

calculus developed by R. Coifman and Yves 

Meyer in the 1980’s. Moving to functions of two variables, 

consider a Leibniz rule for differentiation in two coordinates 

given by 

This inequality is true, and follows from the two-parameter 

version of the Coifman-Meyer Theory. Initially studied by 

Jean-Lin Journe, this subject has been extended and recast 

in recent work of Camil Muscalu, Pipher, Terrence Tao and 

Christoph Theile. 

One can consider more sophisticated Leibniz rules. They in 

turn would follow from more sophisticated variants of the 

product theory, in which singularities of the corresponding 

operators are best described by a flag that is a decreasing 

family of subspaces. This theory, in its nascency, could be 

the subject of future Coxeter Lectures. 

Michael Lacey 

< 

≤ 

DISTINGUISHED LECTURE SERIES 

Uffe Haagerup (Odense): 

Free probability and the invariant subspace problem for von 

Neumann algebras 

November 6, 7 & 8, 2007 

The Invariant Subspace Problem is perhaps the most 

famous open problem in functional analysis. In its present 

form, it asks whether every bounded linear operator T on 


a separable Hilbert space H has a non-trivial invariant 

subspace, i.e., a subspace M of H such that T(M) ⊆ M. 

(The question was originally formulated with an arbitrary 

Banach space X in place of H, and was shown to have a 

negative answer by Per Enflo in the 1970s.) Uffe Haagerup’s 

Distinguished Lecture Series, held on November 6, 7, and 

8, 2007, described his remarkable results, joint with Hanne 

Schultz, on a still harder problem than the usual Invariant 

Subspace Problem, namely, the invariant subspace problem 

relative to a factor. 

A von Neumann algebra is a self-adjoint subalgebra of the 

algebra B(H ) of bounded linear operators on H which is 

closed in the strong operator topology (SO): 

T n 

⎯ ⎯ → 

) (SO) 

(S O 

T ⇔ Tnξ T 

→ ξ, ∀ξ ∈ H 

If M is a von Neumann algebra whose center consists only 

of scalar operators, then we say that M is a factor. Thus, 

B(H ) is a factor for any Hilbert space H. The study of von 

Neumann algebras was initiated by Frank Murray and Jon 

von Neumann in the 1930s, and among their first results 

was the classification of factors into five types. Their classification 

is simple enough to describe here. 

Let M be a factor. A self-adjoint idempotent p ∈ M is 

called a projection, and we denote the set of these by 

Proj(M ). We say that projections p,q ∈ M are Murrayvon 

Neumann equivalent if there is some v∈ M such that 

v*v = p and vv* = q. A dimension function on M is a map 

D: Proj(M ) → R 

+ { ∞ } 

⊂ 

which is constant on Murray-von Neumann equivalence 

classes, and which is additive on sums of orthogonal 

projections, i.e., D(p + q) = D(p) + D(q) whenever pq = 0. 

Murray and von Neumann proved that every factor admits 

a dimension function which is unique up to scaling, and 

that the possibilities for the range of D are as follows: 

Type I n : D(Proj(M)) = {0,1,…,n} 

Type I ∞ : D(Proj(M)) = {0,1,…, ∞ } 

Type II 1 : D(Proj(M)) = [0,1] 

Type II ∞ : D(Proj(M)) = [0, ∞ ] 

Type III: D(Proj(M)) = {0, ∞ } 

If M is a von Neumann algebra acting on a Hilbert space 

H, M is a subspace of H, and the projection of H onto M 

belongs to M, then we say that M is affiliated with M. M 

is non-trivial if M ≠ {0} and M ≠ H. If T: H → H is a 

bounded linear operator, then M is T-invariant if T(M) ⊆ 

M, and T-hyperinvariant if it is S-invariant for every S ∈ 

B(H ) such that ST = TS. 

33


34 

uffe haagerup and Juris Steprans 

The invariant subspace problem relative to M asks whether 

every T ∈ M has a non-trivial invariant subspace M 

affiliated with M, and the hyperinvariant subspace problem 

asks whether M can always be chosen hyperinvariant for T. 

The usual formulation of the Invariant Subspace Problem 

appears in this framework as the invariant subspace problem 

relative to the factor B(H ) for H separable. 

Haagerup’s Distinguished Lecture Series presented a nearly 

complete solution to the invariant subspace problem relative 

to a factor of Type II 1 , a result he obtained jointly with 

Hanne Schultz. To state the main result, we require the 

notion of Brown measure. 

A factor M of Type II 1 has a unique tracial state τ: M → C, 

i.e., a positive linear functional such that τ(1 M ) = 1 and 

τ(xy) = τ(yx) for every x,y ∈ M. Using it one defines the 

Kadison-Fuglede determinant, ∆ : M → [0, ∞ ), by the 

following formula: 

∆(T) = exp(τ(|T|)), 

with exp(– ∞ ) ≡ 0. (The operator |T| is the positive part 

of the polar decomposition for T, and is given by the formula 

|T| = (T*T) 1/2 .) It was shown by Larry Brown that the function 

λ log ∆(T –λ1) 

is subharmonic in C, and its Laplacian 

d µ T (λ 1 + iλ 2 ) = 1 

2π ∇2 log ∆(T – (λ 1 + iλ 2 )1)dλ 1 dλ 2 

defines a probability measure µ T on C supported in the 

spectrum σ(T) of T. This is called the Brown measure of 

T. If T is normal, then τ induces a probability measure 

on the spectrum of σ(T) via the spectral theorem; the 

norm-closed subalgebra of M generated by 1, T and T* is 

isomorphic to the algebra of continuous C-valued functions 

on σ(T), and traces on this algebra – in particular, the 

trace induced by restricting τ – correspond to probability 

measures on σ(T). The measure on σ(T) induced by τ is the 

Brown measure of T. 

Theorem 1 (Haagerup-Schultz, 2005). Let M be a factor of 

Type II 1 . For every T ∈ M and every Borel set B ⊆ C, there 

is a largest closed, T-invariant subspace K = K T (B) affiliated 

with M such that the Brown measure µ T| K is concentrated 

on B. K is moreover T-hyperinvariant, and if P = P T (B) ∈ 

M denotes the projection from H onto K, then 

(i) τ(P)= µ T(B) , and 

(ii) the Brown measure of P ⊥ T P ⊥ , relative to P ⊥ M P ⊥ , is concentrated 

on C \ B. In particular, if µ T is not a Dirac measure, 

then T has a non-trivial hyperinvariant subspace affiliated 

with M. 

Let us now describe the hyperinvariant subspace KT (B) of 

the theorem. For r > 0, let E(T,r) be the set of vectors ξ ∈ 

∞ 

H for which there is a sequence (ξn ) n=1 in H such that 

lim ||ξ n – ξ||= 0 and lim sup ||(T – 1) n ξ n || 1/n ≤ r. 

Define F(T,r) to be the set of vectors η ∈ H for which 

there is a sequence (ηn ) n=1 in H such that 

lim ||(T –1) n ∞ 

ηn – η|| = 0 and lim sup ||ηn || 1/n 1_ ≤ 

r 

. 

n → ∞ 

The bulk of the difficulty in proving the main theorem is 

overcome by showing that 

and 

K T (B(0,r)) := E(T,r) 

K T (C \B(0,r))) := F(T,r) 

satisfy the conditions of the main theorem in the cases B = 

B(0,r) and B = C \ B(0,r), respectively. To obtain KT (F) for 

F ⊆ C closed, one writes C \ F as a countable union of open 

balls 

and proves that 

C \ F = B( n , r n ) 

 

KT (F) := F(T – n1, rn ) 

has the properties required by the theorem. Finally, for B 

arbitrary Borel, it is proved that 

does the trick. 

∞ 

n =1 

∞ 

n =1 

n → ∞ 

K T (B) := K T (H) 

H⊆B,H compact 

One surprising consequence of the proof of the main theorem 

is this: in the case where the Borel set B of the theorem 

is of the closure of either B(0,r) or C \ B(0,r), then the 

projection P K (B) can be realized as a spectral projection. 

Explicitly:

Theorem 2 Let M of Type II 1 . For every T ∈ M we have 

the following: 

(a) There is a unique positive operator A ∈ M such that 

P E(T,r) = [0,r] (A). 

Moreover, A is the limit, in the strong operator topology, of the 

sequence ((T*) n T n ) 1/2n . 

(b) There is a unique positive operator B ∈ M such that 

P F(T,r) = [r,∞] (B). 

Moreover, B is the limit, in the strong operator topology, of the 

sequence (T n (T*) n ) 1/2n . 

It is already interesting that the strong operator limits of 

the sequences ((T*) n T n ) 1/2n and (T n (T*) n ) 1/2n always exist 

for T in a factor of Type II 1 , as these limits do not exist for 

general T ∈ B(H ). 

Haagerup’s first lecture gave an introduction to the invariant 

subspace problem relative to a factor, and described 

the main results obtained with Schultz. In his second 

talk, the proof was discussed in some detail. These details 

are perhaps too much for the present article, but let us at 

least point out that they involve a remarkable breadth of 

techniques from non-commutative analysis. These include 

Voiculescu’s free probability theory and Turpin-Waelbrock 

integration on quasi-normed spaces. In the final lecture, 

some applications of the main result were described, as 

were some related results on invariant subspaces for various 

types of operators obtained by Haagerup in joint works 

with Dykema, Larsen, and Schultz. In particular, it was 

shown that every factor of Type II 1 contains an indecomposable 

operator (joint with Schultz). 

Andrew Toms 

Timothy Gowers (Cambridge) 

Quadratic Fourier Analysis 

April 9–11 2008 

Timothy Gowers, Rouse Ball Professor of Mathematics 

at Cambridge and a 1998 Fields Medalist, is one of the 

founders of – and unquestioned leaders in – additive 

combinatorics. His work on Szemerédi’s theorem has 

transformed the field and opened the way to many further 

developments, including the Green-Tao theorem and quantitative 

versions of combinatorial results previously only 

available in a qualitative form. His ideas have found their 

way into several other areas of research, from harmonic 

analysis to theoretical computer science. 

Lectures and Special Events 

Jaroslav nesetril and Jean Bourgain 

Gowers spoke on “quadratic Fourier analysis”, a subject 

that goes back to his 1998 proof of Szemerédi’s theorem and 

continues to be developed by many authors, with major contributions 

by Green, Tao, Samorodnitsky, and Gowers himself. 

In his first lecture, addressed to a general audience, Tim 

gave an introduction to U d uniformity and inverse theorems. 

Suppose that we want to prove Szemerédi’s theorem: 

if a set A⊂ Z contains a positive proportion of integers, then 

it must contain a k-term arithmetic progression for each 

k. The general strategy is well known by now. If A is randomly 

distributed, in the sense that it does not exhibit any 

noticeable “special patterns”, then there are many k-term 

progressions in A. If on the other hand A is not random, 

we take advantage of that by choosing structured subsets of 

integers on which A has higher density. Iterating the argument, 

we eventually prove the theorem. 

Exactly what it means for a set to be random, or to exhibit 

a special pattern, depends in a crucial way on the length k 

of the progression that we are looking for. It also depends, 

to a somewhat lesser extent, on the choice of approach 

to Szemerédi’s theorem: graph-theoretic, ergodic, or 

harmonic-analytic. We will focus on the harmonic-analytic 

proof, due to Roth for k = 3 and to Gowers for general k. 

Here, uniformity is defined in terms of the so-called U d 

Gowers norms: if a set is uniform with respect to the U k-1 

norm, it contains the statistically correct number of k-term 

arithmetic progressions. 

U 2 -uniformity, also known as linear uniformity, has a 

Fourier-analytic interpretation. If A is not U 2 -uniform, its 

characteristic function has a large Fourier coefficient; in 

other words, A correlates with a phase function, where (x) 

is linear. (This is where the terminology comes from: a set 

is linearly uniform if and only if it has no linear patterns.) 

What about U 3 -uniformity? It has been known for some 

time (due perhaps to Furstenberg and Weiss) that a set of 

35


integers can have a statistically disproportional number 

of 4-term arithmetic progressions if it exhibits “quadratic 

patterns”, in the sense that its characteristic function correlates 

with e 2πi(x) , where is a quadratic homomorphism. 

(Quadratic homomorphisms are somewhat more general 

than quadratic polynomials in x: they also include linear 

projections of quadratic polynomials in several variables.) 

Similarly, higher degree polynomial patterns contribute to 

U d -nonuniformity for higher d. 

What we need in the proof of Szemerédi’s theorem is an 

inverse theorem: if a set is not U d -uniform, it must exhibit 

a polynomial pattern. This turns out to be very difficult to 

prove. The first such result for d ≥ 3 was proved by Gowers; 

his result is sometimes known as a weak inverse theorem, 

in the sense that the polynomial correlations occur only 

on very small parts of the set. Other applications require 

stronger inverse theorems: in particular, Tim mentioned 

the Green-Tao inverse theorem for the U 3 norm and its 

application to counting 4-term arithmetic progressions in 

the primes. That’s where the first lecture ended. 

In the second lecture (based on Gowers’s joint work with 

Julia Wolf) we were introduced to decomposition theorems. 

A decomposition theorem for the U 3 norm can be stated 

n 

as follows: if f is a function (on either ZN or Fp ) with ||f||2 

≤ 1, there is a decomposition f = iQi + g + h, where the 

Qi are “generalized quadratic phase functions” and g and h 

are error terms with || g || U 3 and || h ||1 small. This can be 

deduced from the U3 inverse theorem of Green-Tao; in fact, 

a similar statement was already implicit in their work. Tim 

presented a new approach to deducing decomposition theorems 

from inverse theorems, based on functional-analytic 

arguments involving the geometry of normed spaces and, 

specifically, a variant of the Hahn-Banach theorem. 

This can be applied to the question of counting solutions 

to systems of linear equations in sets. Suppose that we are 

interested in finding sensible conditions under which a set 

A⊂ F p n will have the statistically correct number of solutions 

to a system of linear equations. For instance, it is well 

known that U 3 -uniformity guarantees the right number of 

4-term arithmetic progressions x, x+r, x+2r, x+3r. Green 

and Tao prove a more general result of this type: they introduce 

the notion of complexity of a system of linear forms 

and prove that systems of complexity k are controlled by 

U k+1 norms. 

Gowers and Wolf, however, do not stop there. Suppose that 

we are interested in counting configurations of the form, 

say, x, y, z, x+y+z, x-y+2z, x+y-2z. The complexity of this 

36 

system in the sense of Green-Tao is 2, hence a set A uniform 

with respect to the U 3 norm will contain the “right” 

number of such configurations. Gowers and Wolf, however, 

can prove that U 2 -uniformity already guarantees the same 

conclusion! Why is this example different from 4-term 

progressions? The squares x 2 , (x+r) 2 , (x+2r) 2 , (x+3r) 2 are 

linearly dependent, whereas x 2 , y 2 , z 2 , (x+y+z) 2 , (x-y+2z) 2 , 

(x+y-2z) 2 are not. Gowers and Wolf prove that such “square 

independence” is in fact both sufficient and necessary for 

a system of complexity 2 to be controlled by the U 2 norm. 

The proof is based on the decomposition theorem described 

earlier. 

The last lecture focused specifically on the Hahn-Banach 

type functional-analytic arguments. Tim started out by 

explaining parts of the proof of the decomposition theorem 

from the second lecture, then went on to present further 

applications of the Hahn-Banach approach. One concerns 

a new proof of the transference principle of Green-Tao 

and Tao-Ziegler, based on functional-analytic arguments 

instead of the more involved energy-increment iteration. (I 

learned later that a similar approach had also been developed, 

independently and around the same time, by Omer 

Reingold, Luca Trevisan, Madhur Tulsiani and Salil Vadhan, 

who were motivated by certain questions in computer 

science.) The second application is a refinement of Tao’s 

“structure theorem” from his quantitative version of the 

ergodic-theoretic proof of Szemerédi’s theorem. 

Izabella Łaba 

Alain Connes (Collège de France, IHES & Vanderbilt University) 

May 28, 29, 30–2008 

Alain Connes (Fields Medal 1982, Crafoord Prize 2001, 

CNRS gold medal 2004), delivered a series of three lectures 

from May 14 to 17, 2008 at the Fields Institute. The 

lectures took place during the Fields Institute conference 

on noncommutative geometry. It was the second time that 

Connes gave a distinguished lecture series, the first being in 

1995. It was fascinating to appreciate how much the subject 

has evolved in the past 10 years alone. The overall theme 

of these lectures was Noncommutative Geometry (NCG), a 

subject created by Connes himself during the last 30 years 

and currently studied by many researchers around the 

globe. The talks were titled The spectral characterization of 

manifolds, A CKM invariant in Riemannian geometry and 

About the field with one element.

I can broadly say that noncommutative geometry is the 

mathematics needed for the study of noncommutative 

spaces. These ‘spaces’ are usually represented by a noncommutative 

algebra (usually plus some additional structure) 

replacing the algebra of coordinates in the classical commutative 

case. Examples include highly singular spaces 

such as the space of leaves of a foliation, the unitary dual of 

a noncompact group, and more generally, ‘bad quotients’ of 

nice spaces. This is not a place to survey the development of 

NCG, even a quick account of which would require many 

pages. It suffices to say that the subject has gone through 

three phases so far. In its initial stage NCG was mostly 

inspired by global analysis, topology, operator algebras and 

quantum physics, as they show up in areas such as index 

theory, foliation theory, quantum statistical mechanics, and 

its main application was to settle some long standing conjectures 

such as the Novikov conjecture in topology. Next 

came the impact of spectral geometry and the way the spectrum 

of a geometric operator like the Laplacian informs 

us about the geometry and topology of a manifold, e.g. as 

in the celebrated Weyl’s Law. This is now subsumed and 

vastly generalized through Connes’ notion of spectral triples 

which is a centerpiece of noncommutative Riemannian 

geometry and applications of noncommutative geometry to 

particle physics. Finally, in recent years we have witnessed 

the impact of number theory, algebraic geometry and the 

theory of motives and quantum field theory on NCG, and a 

strong interaction between these areas. One major goal here 

is to understand the set of prime numbers as a geometric 

space, and apply this vision to the study of the zeros of the 

zeta functions and L-functions. 

In his first lecture Connes explained his very recent 

Reconstruction Theorem which is about a spectral characterization 

of smooth manifolds and fully justifies his notion 

of noncommutative Riemannian manifold. He showed that 

the first five axioms he had given in 1996 on the spectral 

triples suffice in the commutative case to characterize 

smooth compact manifolds. To appreciate this result, I 

recall that one of the first lessons of the theory of operator 

algebras is that commutative C*-algebras (resp. von Neumann 

algebras) correspond to locally compact topological 

spaces (resp. Borel measure spaces). To get an appropriate 

notion of a noncommutative smooth manifold and smooth 

structures one must plunge in deeper waters and look for 

ideas in spectral geometry and Dirac’s equation which are 

the source of these axioms. In the first part of his second 

lecture, Connes defined a new invariant in Riemannian 

geometry, which when combined with the spectrum of the 

Dirac operator is a complete invariant of the geometry. It 


is an analogue of the CKM mixing matrix of the Standard 

model. The remaining part of the second lecture was 

devoted to a noncommutative geometric description of the 

Lagrangian of the standard model of elementary particle 

physics. The full Lagrangian, including the electro-weak 

and strong sectors with symmetry group U(1) × SU(2) × 

SU(3) is a marvel of modern science and the result of many 

years of hard work by experimentalists and theoreticians. 

Connes showed how this Lagrangian can be derived from 

a very basic spectral action principle for spectral triples on 

a noncommutative algebra. The noncommutative algebra 

of coordinates is uniquely defined through the group of 

symmetries of the theory. It is a product M × F of space 

time with a finite dimensional noncommutative space F 

responsible for quantum fluctuations. It is amusing to note 

that this very Lagrangian is now put to a final test by the 

LHC machine at CERN, Switzerland, to try to find the last 

piece of the puzzle, the Higgs particle, which is predicted 

by theory but not yet observed. In his last lecture Connes 

described his joint work with C. Consani and M. Marcolli 

which relates the mysterious and illusive “field with one 

element” to quantum statistical mechanics, more explicitly 

to the Bost-Connes system. Every undergraduate student of 

mathematics knows that a field, by definition, must have 

at least 2 elements, so that a field with one element does 

not exist in the usual sense. A deep insight of Jacques Tits 

arising in his work on Chevalley groups back in 1950’s 

convinced him that some of these groups can be fruitfully 

thought of as automorphism groups of projective spaces 

over a fictitious field with one element. That is, there 

should exist an algebraic formalism which would play the 

role of a “field of characteristic one”, as he would call it, 

as a degeneration of a finite field with q elements as q ! 1. 

Later the need for a field with one element arose in a totally 

different way in Arakelov geometry and in the study of 

the zeros of zeta and L-functions. One idea is to create an 

environment where Weil’s proof of the Riemann hypothesis 

for algebraic curves over finite fields could be mimicked 

and extended to a proof of the Riemann hypotheses for the 

original Riemann zeta function. This approach, as Connes 

explained in his last lecture, requires regarding Spec Z as a 

variety over a field with one element. The Bost-Connes system 

on the other hand is a quantum statistical mechanical 

system in the context of noncommutative geometry which 

encodes prime numbers. It allows, after passing to the dual 

system, a spectral realization of the zeros of the Riemann 

zeta function as its partition function, as well as a trace formula 

interpretation of the Riemann-Weil explicit formulas. 

Connes showed how the inductive structure of the algebraic 

37


closure of this mysterious field with one element gives rise 

to this quantum statistical mechanical system. This natural 

appearance of the BC system through the field with one 

element gives further evidence to the importance of the 

Bost-Connes system for number theoretic investigations. 

Masoud Khalkhali 

DISTINGUISHED LECTURE SERIES IN 

STATISTICAL SCIENCE 

Persi Diaconis (Stanford) 

Magic and mathematics 


Persi Diaconis, Mary V. Sunseri Professor of Statistics and 

Mathematics at Stanford University, was this year’s speaker 

in the annual Distinguished Lecture Series in Statistical 

Science, adding to an impressive list of previous speakers 

such as Elizabeth Thompson, Bradley Efron, David Cox, 

and Donald A.S. Fraser. 

A member of the National Academy of Sciences, recipient 

of numerous honorary degrees as well as the MacArthur 

fellowship, Diaconis has had a unique career. After beginning 

as a magician at the age of fourteen under the tutelage 

of Dai Vernon, he encountered Feller’s famous book a 

decade later and was enticed into the field of probability 

and statistics. His scientific contributions include a study of 

mixing times of Markov chains, the cut-off phenomenon, 

Bayesian statistics, the use of group representations to study 

card shuffling, random matrix theory, exposing psychics, 

debunking paranormal phenomena, and much more. 

The first lecture, Mathematics and magic tricks, was delivered 

to an audience that overflowed the main lecture hall, 

spilling into two adjacent rooms. In his book Flim-Flam, a 

conjurer no less than James Randi declares, “Persi is capable 

of miracles with a deck of cards that would put to shame 

many a professional magician.” Thus, it was a rare treat for 

the audience that Diaconis began his lecture by performing 

a card trick he invented more than twenty years ago. In 

a bare outline that cannot do justice to the charm of the 

actual performance, the trick involved a sequence of five 

people picking five consecutive cards from a deck, after 

which, with additional information as to the colour of the 

card each person held, Diaconis demonstrated how to guess 

the card picked by each. This is achieved by having the 

32-card deck arranged in advance in such a way that each 

of the 2 5 = 32 possible sequences of colours (red or black) of 

length five occurs exactly once–this is called a “de Bruijn 

38 

persi Diaconis 

sequence.” During the rest of the lecture Diaconis talked 

about counting the number of de Bruijn sequences, how to 

construct one of them, 2-dimensional generalizations, and 

analogous sequences involving other combinatorial structures. 

Not least, the audience learned to seek magic tricks 

when faced with a combinatorial sequence that contains a 

number close to fifty-two! 

The second lecture, Gibbs sampling, orthogonal polynomials 

and alternating projections, led deeper into the waters of 

probability theory. A standard tool in scientific computing 

is the simulation of random systems, and except in trivial 

applications, this is usually done by running a Markov 

chain whose stationary distribution is the measure that one 

wants to sample from. The Gibbs sampler is a widely used 

method of constructing a Markov chain for a given stationary 

measure. For instance, to sample from a density f(x,θ), 

one fixes θ and samples x from its conditional distribution 

and vice versa. In spite of its wide applicability, the theoretical 

analysis of such chains is in a primitive stage. Diaconis, 

along with co-authors Laurent Saloff-Coste and Kshitij 

Khare, analysed convergence to stationarity very precisely 

for the Gibbs sampler in specific situations involving 

conjugate prior distributions. The analysis also revealed a 

connection with a theorem of von Neumann on alternating 

projections, a result from the area of operator theory. This 

is unsurprising to probabilists who are used to being surprised 

by Diaconis’s ability to find results in distant areas of 

mathematics and make use of them in concrete problems. 

Another characteristic trait of his research that was also 

emphasized in these lectures was the avoidance of easy limit 

theorems, aiming instead at getting explicit, usable answers. 

Manjunath Krishnapur

2008 CRM-FIELDS-PIMS PRIzE LECTURE 

Allan Borodin (Toronto) 

Understanding Simple Algorithms: Toward a More Systematic 

Study of Algorithms 

April 28, 2008 

Allan Borodin of the University of Toronto has been 

awarded the 2008 CRM-Fields- PIMS prize. According to 

the citation “Professor Borodin is a world leader in the mathematical 

foundations of computer science. His influence on 

theoretical computer science has been enormous, and its scope 

very broad. Jon Kleinberg, winner of the 2006 Nevanlinna 

Prize, writes of Borodin, “he is one of the few researchers for 

whom one can cite examples of impact on nearly every area 

of theory, and his work is characterized by a profound taste in 

choice of problems, and deep connections with broader issues 

in computer science.” Allan Borodin has made fundamental 

contributions to many areas, including algebraic computations, 

resource tradeoffs, routing in interconnection networks, 

parallel algorithms, online algorithms, and adversarial queuing 

theory.” 

Borodin received his B.A. in Mathematics from Rutgers 

University in 1963, his M.S. in Electrical Engineering & 

Computer Science in 1966 from Stevens Institute of Technology, 

and his Ph.D. in Computer Science from Cornell 

University in 1969. He was a systems programmer at Bell 

Laboratories in New Jersey from1963-1966, and a Research 

Fellow at Cornell from 1966-1969. Since 1969 he has taught 

with the computer science department at the University 

of Toronto, becoming a full professor in 1977, and chair of 

the department from 1980-1985. He has been the editor of 

many journals and managing editor of the SIAM Journal of 

allan Borodin 


Computing, Algorithmica. He has held positions on dozens 

of committees and organizations, both inside and outside 

the University, and has held several visiting professorships 

internationally. In 1991 Borodin was elected a Fellow of the 

Royal Society of Canada. 

A common theme in Borodin’s research is that he explores 

fundamental questions that should be well understood but 

often defy answers to even the most basic aspects of these 

questions. As a result, he has often been at the forefront of 

developing new models and problem formulations that have 

become standard frameworks for computer science studies. 

Perhaps the most basic scientific aspect of computer science 

is to understand the intrinsic limitations of what can and 

what cannot be efficiently computed in various models of 

computing with respect to various measures of complexity. 

At the heart of complexity theory is the study of the 

intrinsic limitations of efficient computation. The other 

side of the complexity theory coin is the design and analysis 

of algorithms. Borodin has been involved in both sides of 

this coin since his Cornell Ph.D thesis, in which he studied 

the time complexity classes introduced by Hartmanis and 

Stearns and the more abstract complexity measures axiomatized 

by Blum. 

Borodin soon became more focused on the complexity 

of specific functions and, in particular, what we now call 

“algebraic complexity theory”. The complexity world was 

basically unchartered territory at the end of the 1960s 

although many surprising and widely applicable results 

(for example, the Fast Fourier Transform) were well known 

before the emergence of complexity theory. A number of 

results accelerated the development of complexity theory. 

One such result was Cook’s formulation of the class NP and 

the identification of NP complete problems which became 

and still remains the main evidence that many common 

combinatorial problems cannot be solved efficiently. In 

contrast, Strassen’s surprising result that matrix multiplication 

can be computed in O(n log 2 7 ) arithmetic operations 

showed that our intuition cannot be trusted. Following 

Strassen, Borodin proved a number of results helping to 

establish the field of algebraic complexity. Resurrecting 

a question by Ostrovsky, Borodin showed that Horner’s 

polynomial evaluation is the only method that can achieve 

the optimal 2n arithmetic operations. Since (even with 

preconditioning) n/2 multiplications/divisions and n additions/subtractions 

are required for one evaluation for most 

degree n polynomials, how many operations are needed to 

evaluate a degree n polynomial at n arbitrary points? When 

the evaluation points are the powers of a primitive n th root 

39


of unity, the FFT performs these evaluations in O(nlog n) 

operations rather than the obvious O(n 2 ) operations. By 

reduction to Strassen’s matrix multiplication, Borodin and 

Munro showed that O(n 1.91 ) operations are sufficient. Then 

Borodin and Moenck showed that O(nlog n) non scalar 

multiplications and O(nlog 2 n) total operations are sufficient, 

which was then matched by Strassen’s O(nlog n) lower 

bound for non scalar multiplications. The lower bound uses 

Bezout’s Theorem on the degree of an algebraic variety to 

generalize the obvious fact that an n th degree polynomial 

requires log n multiplications. In an analogue to the degree 

bound, Borodin and Cook show that the number of real 

roots of a polynomial is bounded by the minimal number 

of additions used to compute the polynomial. Beyond these 

research contributions, Borodin and his first Ph.D. student 

Ian Munro wrote the seminal text in the area of algebraic 

complexity and it remained the authoritative source for 

approximately 20 years. 

Another Borodin interest concerns parallel computation 

and network routing. Following the known results relating 

sequential time with circuit size, Borodin showed that the 

space measure is directly related to uniform circuit depth, a 

basic measure of parallel complexity. Many parallel computation 

models have been studied, including various parallel 

RAM models and interconnection network models. In 

order for an interconnection network to simulate a PRAM, 

the network must simply and efficiently rout simultaneous 

messages. Oblivious routing schemes are simple in that 

the path of each message is independent of other messages. 

Valiant showed that by obliviously routing to a random 

intermediate node, any permutation can be routed in time 

O(d) on a d-dimensional hypercube. This is optimal since 

d is the diameter of the network. Borodin and Hopcroft 

showed that this use of randomness is necessary in the following 

strong sense: in any n node network of degree d, for 

any deterministic oblivious routing algorithm, there exists 

a permutation that will have a bottleneck node forcing at 

least O routing time. Borodin was also the codesigner 

of some surprising parallel algorithms, including 

(with von zur Gathen and Hopcroft) a randomized parallel 

greedy algorithm to derive a log 2 n parallel time algorithm 

for the rank of an n × n matrix, and (with Hopcroft) a log 

log n algorithm for merging two lists on a PRAM. 

Packet routing can be viewed as a queuing system in which 

the network edges become the servers. In this setting, input 

requests (e.g. oblivious packet paths or requests for packet 

transmission along any path from source to target) are 

characterized more by burstiness rather than by any stan- 

40 

dard probabilistic distribution. Borodin, et al modeled this 

burstiness by an adversarial model and developed a new 

research area named “adversarial queuing theory”. There 

are some natural queuing limitations on stability (i.e. time 

to complete a transmission) with the main limitation (in 

oblivious routing) being that the rate of requests for an edge 

cannot exceed the edge processing rate. Borodin et al began 

the study as to which networks are always stable (independent 

of the scheduling rule) and which scheduling rules 

are always stable (independent of the network). Adversarial 

studies of packet routing and other queueing systems has 

led to a number of surprising results (e.g. the instability of 

FIFO at any rate for certain networks as shown by Bhattacharjee 

and Goel). 

While complexity theory has been very successful in many 

aspects (e.g. understanding the relation between complexity 

measures, complexity based cryptography, interactive 

proofs and probabilistically checkable proofs), the major 

limitation of the field remains the inability to prove 

complexity impossibility results for problems such as NP 

search and optimization problems. Indeed, non-linear time 

bounds (on a sufficiently general model of computation) or 

space bounds greater than log n still elude us. Perhaps then 

the simplest barrier to break is to exhibit a problem which 

cannot be simultaneously computed in small time and 

space. Borodin and coauthors prove the first time-space 

tradeoff result for comparison based sorting in the most 

general model for such a result. They considered comparison 

branching programs which are DAGS where nodes are 

labelled by comparisons “a i ≤ a j ?” between elements from 

a given “read-only” input set of n elements. In this model, 

edges are labelled by sequences of input elements that are 

output if this edge is traversed. The sequence of outputs 

along any path defines the output of the program. In this 

non-uniform model (like circuits, a different program is 

allowed for each n), time is the length of the longest path, 

and space is the logarithm of the number of nodes (i.e. the 

information theoretic lower bound on the memory). In 

contrast to merging, which can be computed simultaneously 

in linear time and O(log n) space, Borodin et al show 

that the time space product T · S = O ( n 2 ); that is, any 

small space method requires significantly more time than 

the optimal nlog n bound achievable by methods such as 

merge-sort. (For all space bounds S(n) between log n and n, 

a corresponding upper bound can be obtained.) 

The time space paper was seminal and started a long and 

continuing research effort to derive time space bounds 

for natural problems in appropriate models. The sorting

tradeoff was followed by a similar comparison branching 

program tradeoff for a decision problem, namely element 

distinctness. The initial element distinctness tradeoff was 

by Borodin and co-authors, and then improved by Yao. 

These comparison branching programs (which do not have 

access to the encoding of input elements) leave open the 

possibility that the corresponding Boolean problems (e.g. 

encoding integer inputs in binary) can be computed using 

simultaneously small time and space. This consideration 

led Borodin and Cook to introduce the R-way branching 

program model, where now inputs are considered to be 

integers in some range [1,R], and branching program nodes 

are of the form “ai = ?”, with up to R branches corresponding 

to each possible value for ai. Borodin and Cook showed 

that sorting n numbers in the range [1, n 2 ] requires T · S 

= O( n 2 ), proving a strong tradeoff result. This represents 

the first negative result for an explicit Boolean problem in 

a completely general model, albeit not a decision problem. 

It took approximately 20 more years to establish negative 

results (of a much weaker form) for a Boolean decision 

problem. 

In the mid 1980s, Borodin began working on the competitive 

analysis of online algorithms, whereby the performance 

of an online algorithm making decisions for each input as it 

arrives is compared to the performance of an optimal solution 

with knowledge of the entire input. There had been a 

number of earlier results concerning online algorithms for 

specific problems that need not necessarily be considered 

as online problems (for example, Graham’s study of the 

makespan problem, Yao’s study of online bin packing). Sleator 

and Tarjan proposed competitive analysis (in contrast 

to distributional studies) for inherently online problems 

such as paging and list accessing. Borodin, Linial and Saks 

proposed an abstract online problem framework called 

metrical task systems (MTS) which was soon followed by 

the k-server model of Manasse, McGeouch and Sleator. The 

introduction of competitive analysis for online problems 

and these abstract problem formulations spawned a wealth 

of research activity that has had an impact well beyond 

online problems. The BLS paper provides an optimal 2n - 1 

competitive ratio bound for deterministic algorithms for 

any n-state MTS. It also introduced randomized algorithms 

in this context showing that the uniform metric system had 

a 2H n randomized competitive ratio. This led the way to a 

randomized paging algorithm by Fiat et al and, moreover, 

led to interest in trying to derive randomized algorithms 

for general MTS and k-server problems. In this context 

Bartal introduced Hierarchically Separated Tree spaces 

(HSTs) for which O(log n) randomized algorithms exist 


and furthermore arbitrary metric spaces can be efficiently 

embedded into HSTs. The use of HSTs has now become a 

standard tool in combinatorial approximation. 

Beyond the seminal MTS work, Borodin was influential 

in other central results concerning competitive analysis. 

Borodin et al introduced a variant of competitive analysis 

so as to model the locality of reference exhibited by (for 

example) paging requests. Another landmark paper introduces 

“request-answer games”, a framework for defining 

most known online problems. In this very general setting 

(including the MTS and k-server settings), Borodin and 

coauthors relate the power of different adversarial models 

for randomized online algorithms; namely, they identify 

the standard oblivious adversary (as used in offline computation) 

where the adversary generates the input request 

sequence without knowledge of the algorithm’s coin tosses, 

and adaptive adversaries where the adversary adaptively 

creates the input sequence by observing the coin tosses and 

actions of the online algorithm. For adaptive adversaries, 

the adversary (acting also as the “optimal benchmark”) can 

either play the game online or in hindsight as an offline 

player. Ben David et al show that algorithms competing 

against online adaptive adversaries can be simulated by 

algorithms competing against offline adaptive adversaries 

which in turn can be simulated by deterministic algorithms 

thereby showing that randomization can only yield 

significantly improved competitive ratios for algorithms 

competing against oblivious adversaries. 

Finally one of Borodin’s most influential contributions to 

online analysis is his text with former student Ran El-Yaniv. 

The text (published in 1998) remains the authoritative 

reference for this area, although many significant results 

have followed its publication, including a number of results 

addressing questions raised in the book. 

Borodin has made significant contributions to a number 

of other aspects of algorithm analysis. One paper with 

Ostrovsky and Rabani provides the first memory-search 

time results for problems (e.g. nearest neighbour and 

partial match search) in high dimensional spaces, proving 

that for deterministic algorithms some form of exponential 

“curse of dimensionality” must exist for a widely studied 

geometric search model. 

Borodin’s most recent research area has been an area he has 

essentially been creating, namely the attempt to study the 

power and limitations of “simple algorithms,” especially 

(to date) for search and optimization problems. While 

we equate efficient algorithms with time and/or memory 

41


efficiency, there are other important aspects to algorithm 

design. We often want simple understandable algorithms, 

at least as starting points or benchmarks for developing 

more sophisticated, complex algorithms. We tend to use a 

small set of basic algorithmic paradigms as a “toolbox” for 

an initial (and sometimes the best known or even optimal) 

method for solving large classes of problems in many settings. 

These basic paradigms include greedy algorithms, 

divide and conquer, dynamic programming, local search, 

primal dual algorithms and IP/LP rounding. Surprisingly, 

although we intuitively understand what these concepts 

mean, rarely do we attempt any precise formulation, and a 

precise formulation is necessary if one is to gain any insight 

into the ultimate power and limitations of these methods. 

The pervasive use of greedy algorithms provides a great 

example of an algorithmic paradigm that seems so natural 

and obvious that no definition seems necessary. It is hard 

to think of a computational area where some concept of 

greediness does not appear. The elegant results of Edmonds, 

Korte, Lovasz connecting matroids and greedoids with the 

optimality of “the” natural greedy algorithm for certain set 

systems was the starting point for a number of insightful 

results concerning optimal greedy algorithms. But greedy 

algorithms are mainly used as a heuristic or to obtain 

approximation results. Borodin, Nielson and Rackoff 

introduce the priority algorithm framework as a model for 

“greedy-like” optimization algorithms. In this framework 

an input to a problem is a set of items (for example, jobs in 

a scheduling problem, vertices in a graph problem, propositional 

variables in a SAT problem) and a priority algorithm 

considers and makes decisions about items one by one but 

now in an order determined (in advance or adaptively) by 

the algorithm rather than the order given by (adversarial) 

nature as in online algorithms. The key idea here is to 

formulate what orderings a “reasonable” algorithm can use. 

It would make no sense to allow the algorithm to compute 

an optimal solution and a corresponding optimal order that 

allows the algorithm to produce the optimal solution. One 

could resort to complexity considerations and say that each 

item is chosen within some acceptable time. But that would 

bring us back to our current inability to prove limitations 

based on time complexity. Instead the priority framework 

requires the allowable orderings (at each iteration in the 

case of adaptive priority algorithms) to be local in that they 

satisfy Arrow’s IIA (independence of irrelevant attributes) 

axiom. Whereas in social choice theory this axiom is 

controversial, for greedy-like algorithms the axiom allows 

great generality while still being amenable to analysis. And 

what does this have to do with greediness? In the priority 

42 

framework it is not the ordering decisions that are greedy 

but rather (for greedy priority) it is the decisions being 

made for each input item that can be construed as greedy 

(say in the sense of “living for today”) with respect to the 

given objective function. There are a number of results 

showing the limitations of such priority algorithms in different 

domains, starting with the initial scheduling results 

of Borodin, Nielson and Rackoff. 

The priority framework is also the starting point for more 

powerful paradigms, including simple forms of primal 

dual algorithms using a reverse delete step, simple dynamic 

programming and backtracking. For example, Borodin and 

coauthors show why DPLL style backtracking algorithms 

cannot solve 3SAT search and has limits to approximating 

Max2Sat but can solve 2SAT. They also show that the form 

of dynamic programming used for interval scheduling and 

knapsack algorithms has limitations. In particular, optimal 

dynamic programming algorithms for weighted interval 

scheduling on m machines must suffer a curse of dimensionality 

with respect to m. 

This recent algorithmic design work reflects the style of an 

extraordinarily productive and creative career. 

Stephen Cook

Public Lectures and Special Events 

2 ND ANNUAL NATHAN AND BEATRICE KEyFITz 

LECTURE IN MATHEMATICS AND THE SOCIAL 

SCIENCES 

Jon Kleinberg (Cornell University) 

The Geography of Social and Information Networks 

October 30, 2007 

If you thought that social networking began and ended 

with “six degrees of separation,” and had gotten over being 

impressed with the long way a little random graph theory 

could take you in modelling social phenomena, then Jon 

Kleinberg’s public lecture, The Geography of Social and 

Information Networks, was just the occasion to reawaken 

a sense of wonder in the power of mathematical models 

to organize our complicated lives. Kleinberg, professor of 

Computer Science at Cornell University and most recent 

winner of the IMU Nevanlinna Prize for mathematical 

aspects of information sciences, is the inventor of a field 

now called Algorithmic Sociology. On October 30, Kleinberg 

gave the second Nathan and Beatrice Keyfitz Lecture on 

Mathematics and the Social Sciences to a packed audience in 

Koffler Auditorium. 

The lecture was timed to lead off a week-long symposium 

called Social Networking at the University of Toronto, and 

Jon’s visit also included a Colloquium in the Computer 

Science Department, which explored yet other aspects of 

research in this area–specifically the future of personal 

privacy in a world where it seems that everything is not 

only documented but modelled. More on that later. 

What is a network? Abstractly, a network is a collection 

of objects called nodes connected by links, called edges. 

The objects and links can be actual or virtual. In a “social 

network” the nodes are typically people and the links 

are relations between them: acquaintance, e-mail correspondence, 

spreading a rumour, or dating. Technological 

networks include communications networks, the internet, 

of course, and also road and highway systems–hence “geography”. 

(There are many other examples, not specifically 

touched on in the lecture, such as neuronal networks in the 

brain and body.) Comparisons between social and physical 

networks have led to a rich set of analogies. Kleinberg began 

by noting that these comparisons have led to a convergence 

of social and technological networks since the 1990s. 

In particular, the development of technology has led to 

resolution of social interactions on an unprecedented scale. 


For example, one can watch minute by minute, or month 

by month, the development of information on Wikipedia. 

Digital communication exposes and accelerates many 

forms of interaction. We have at hand details on a range of 

scales, forming a rich data set. 

To begin to develop this theme, Kleinberg introduced the 

notion of maps–good old cartographic maps–as a metaphor 

for the physical world. We are used to this “analogy”: most 

of us can read a map and use it to navigate. In fact, we can’t 

really remember a time in our lives when we did not have a 

mental map-like image of the space in which we move. In 

what terms would we picture a network? Some examples, 

such as the old “Arpanet” (the precursor of the internet, 

that at one time had just thirteen nodes), or a high-school 

dating network analyzed in a public health study, can be 

easily pictured as a graph with nodes and edges as defined 

in graph theory. But once one is dealing with a large 

number of points–the millions of people making up a 

communication network in North America, or the billions 

of nodes on the internet, say–then drawing a picture is no 

longer possible, and the network can be described only with 

the use of mathematics. Thus one arrives at what Kleinberg 

calls “Two lines of research looking for a meeting point.” 

So, back to Stanley Milgram’s experiment; the study that 

launched the term “six degrees of separation.” In that 

experiment, people were asked to get a letter from the 

Midwest to a real person at an address in Massachusetts 

Jon Kleinberg 

43


by sending it only to people they knew personally. It was 

found that the average number of steps was six. And one 

can convince oneself that a pathway of that length might 

exist. But, as many people have asked themselves: How does 

one find it? Kleinberg’s modelling starts with the question 

of how one finds a path from merely local knowledge. As 

is well known, short paths are most easily created by introducing 

a few random links into the network–but that is not 

enough. One needs more structure, and one way to produce 

it (mathematically) is to introduce scaling with distance, so 

that the probability of nodes being connected is inversely 

proportional to some power of the distance between them. 

Then it turns out that an inverse square law is the correct 

scale to allow local information to produce global paths– 

this can be described in terms of scale invariance in planar 

geography. At a final level of abstraction, Kleinberg noted 

that one can generalize the notion of “distance,” replacing 

it by “rank”: number of nodes closer than a given node. 

In the last part of the talk, Kleinberg turned to the topic of 

individual versus group properties. Many social phenomena 

can be described by a distribution of outcomes. Does 

each individual follow the distribution, or is it only in the 

aggregate? As an example, Kleinberg mentioned Barabasi’s 

observation on the distribution of answering e-mail–a 

prediction of the probability distribution of the number 

of days t it takes you to answer an e-mail, given that you 

answer it at all. Out of curiosity, Kleinberg analyzed the 

complete nine-year history of his e-mail correspondence, 

and discovered that he followed Barabasi’s distribution 

exactly. He confessed to a sense of unease at discovering a 

mathematical model that knew things about him he didn’t 

know himself. In fact, he feels that we are going to start 

seeing software that “knows more about you than you do!” 

Kleinberg coined the term “quantitative introspection” 

for this. With some relish, he exhibited a quote from the 

Toronto Globe & Mail of June 2006: “MySpace is doubly 

awkward because it makes public what should be private. It 

doesn’t just create social networks, it anatomizes them. It 

spreads them out like a digestive tract on the autopsy table. 

You can see what’s connected to what, who’s connected to 

whom.” One can make an analogy with an earlier era when 

people objected to anatomical dissecting because it exposed 

things about our bodies that we might be better off not 

knowing. And yet, that opened the era of modern medicine. 

Science moves forward when it “makes the invisible visible.” 

Using the mathematical tools of the new science of 

social network analysis, we will learn a lot both about large 

populations and about ourselves as individuals. But as we 

44 

begin to do so, we have to think about threats to personal 

privacy. 

Those who had been fortunate enough to hear Kleinberg’s 

more technical lecture on protecting privacy earlier in 

the day were now given a context for that topic. Kleinberg 

concluded his lecture with the thought that mathematical 

and computational models will be crucial in resolving these 

concerns. 

Facebook and MySpace are part of the lives of young people, 

and it seems relevant that Jon Kleinberg is part of that 

younger generation. My own children, as teenagers, argued 

passionately about the ethics of downloading and sharing. 

Kleinberg’s last point leads one to realize that ethical concerns 

are going to be central to society’s evaluation of the 

new technologies underlying networks. To many of us, who 

have been able to persuade ourselves that the science we do 

is largely value-free, this marks a change. After spending an 

evening enjoying the prospect that mathematics will come 

more and more to be a critical tool for analyzing phenomena 

in the social sciences–one of the themes of this lecture 

series–it is perhaps important to remember that the study 

of values and how they shape people’s lives is a core area of 

social science. We may find ourselves borrowing here, even 

as we lend our mathematical expertise. 


Fields Institute Grad Day 

November 17, 2007 

For several years the Fields Institute has organized a Saturday 

afternoon event intended to provide information to 

undergraduates considering graduate school in one of the 

mathematical sciences programs of local universities. The 

notion of a local university is beginning to be quite loosely 

interpreted as witnessed by the fact that this year’s participants 

even included members of Concordia University’s 

graduate program in mathematics. Since the number of 

students attending the event is usually around forty, these 

students have ample opportunity to ask many questions 

and engage in a detailed discussion with program representatives. 

It was typical this year for a department’s booth to be visited 

by less than a dozen students interested in its program. 

While some representatives see the value of meeting with a 

small, but self selected group of students who have already 

expressed interest in their program, others wonder whether 

it might not be time to replace Grad Day with a different

type of event. Suggestions along these lines will be enthusiastically 

welcomed. 

The central feature of any Grad Day has always been a talk 

aimed at upper year undergraduates given by an acknowledged 

expert, not only on content but also on presentation. 

Whatever the verdict might be on the outcome of this year’s 

Grad Day as a recruiting vehicle, there is no question that 

the talk by Jeffrey Rosenthal was an unqualified success. 

Rosenthal is well known as the author of a best-selling 

popular book on statistics, Struck by Lightning, as a media 

commentator on matters related to statistics and probability, 

as well as the 2007 winner of the Committee of 

Presidents of Statistical Societies award. This is the most 

prestigious honour bestowed by the COPSS and is awarded 

to a statistician under the age of 40 in recognition of outstanding 

contributions to the profession. 

Much of Jeffrey Rosenthal’s research has been in the area 

of Markov Chain Monte Carlo Methods (MCMC) and he 

decided to explain this statistical technique to the Grad Day 

audience of students and interested colleagues. He began 

with the problem of determining the average height of a 

mountain range by a hiker equipped with an altimeter and 

sturdy boots. The hiker could use MCMC with the following 

procedure: First propose a set of new locations at which 

to perform the height measurement; then select one of these 

proposed locations at random; perform the measurement 

and then continue by proposing a new set of locations at 

which to perform a new height measurement. Each height 

measurement is recorded and a running average is calculated. 

Of course this procedure raises many questions, and the 

keenly attentive audience jumped at the opportunity to 

ask many of these. How does one decide on the proposed 

locations for measurements? Does each proposed location 

have an equal chance at being selected? How many times 

should the process be iterated in order to assure an accurate 

average? What happens if the space being measured is disconnected? 

All of these questions were addressed, but Jeff 

explained that some of them are major open problems in 

statistics and the subject of current research. For example, 

while the Law of Large Numbers implies that the MCMC 

calculates the correct average in the limit—at least it does 

if the set of proposals is chosen carefully—the question of 

when to stop is quite difficult. At the moment, it is common 

in practice to use what are known as convergence diagnostics 

to heuristically determine a stopping time. 


The key concepts of the talk were punctuated with graphic 

applets illustrating the convergence of MCMC and the 

effects of changes in parameters, such as the set of proposals. 

The imagination of the audience had clearly been 

captured and the routine invitation of questions to the 

speaker at the end of the talk resulted in sea of raised hands. 

We will have to wait to see if any of these are answered in 

the doctoral theses of students who attended this year’s 

Grad Day. 

Juris Steprāns 

NERENBERG LECTURE 

Sally Blower (UCLA) 

Sex and HIV: When is it Better to be a Man? 

March 25, 2008 

Held at the University of Western Ontario 

Sally Blower has made a career of constructing mathematical 

models to study the evolutionary dynamics of drug 

resistance. Her research at the David Geffen School of Medicine 

at UCLA has spanned studies into syphilis, genital 

herpes, smallpox, tuberculosis, MRSA, leprosy, trachoma 

and influenza but her main focus is on HIV. 

In countries where AIDS infection rates continue to grow, 

public health organizations remain on the lookout for new 

intervention strategies to halt the spread of HIV. One area 

of research is the use of vaginal microbicides to prevent 

infection in women. There is a lot of hope invested in 

these microbicides and, as Blower says, “they are being 

designed for women to be used by women with the goal of 

empowering women” particularly when these women are 

in a cultural climate that offers little choice. Women who 

are beaten for merely suggesting using a condom may be 

afforded some protection through microbicides. Currently, 

these treatments are in randomized drug trials and are not 

expected to reach the market until 2013. 

What Blower and her colleagues have been doing for the 

last few years is evaluating the benefits of microbicides, 

“which is quite obviously to prevent infections, but also 

evaluate the minuses. It might cause decreased condom use, 

because people might think ‘OK there is a new invention, 

I can use that I won’t use condoms anymore,’ or they can 

generate drug resistance.” 

To answer the questions raised by the combinations of 

these positive and negative factors, Blower constructed 

mathematical models built upon parameters reflecting real 

world situations: the transmissibility of HIV per sex act, the 

45


number of sex acts a female sex worker has with a client, 

the number of clients per day, how well condoms work, how 

well microbicides work, the number of sex acts in which 

each type of protection is used, and the prevalence of HIV 

in the client population. Different probabilities for each 

parameter were then chosen at random and run through a 

mathematical model 10,000 times. 

The models contained a few surprises; Blower showed that 

in certain cases replacing condoms with microbicide “could 

have a high chance of increasing the infections” if the treatment 

has an efficacy of only 30%. If the treatment has at 

least 80% efficacy and the application becomes routine, 

then the real benefits of preventing infection can be seen. 

Blower’s next step was to construct models of clinical trials. 

However, in this analysis there is the added factor of 

acquired resistance, “if you take someone who is infected 

with HIV and you give them antiretroviral drugs” says 

Blower. “What can happen is that the viral load is reduced 

because of the drug but there is still some virus and the 

virus becomes resistant…. Over time the drug sensitive 

virus, the wild type, disappears but the drug resistant 

virus wins out. The treatment is actually selecting for drug 

resistant virus.” Blower also investigated “high-risk” and 

“low-risk” microbicides. The “high-risk” anti-retroviral 

microbicides, Blower says are “the ones that are systemically 

absorbed in the blood and will have a high chance of 

becoming resistant.” As drug trials continue, it is difficult 

to determine which treatments are “high-risk” or “lowrisk” 

because of ethical considerations. In this scenario 

“high-risk” microbicides could pass clinical testing and be 

used as interventions making it impossible to predict the 

population-level consequences beforehand. 

To account for the both high-risk and low-risk microbicides 

Blower constructed two population-level models. Here she 

found a paradox. In both cases, even though the new treatments 

will be used by women to protect themselves from 

infection, it will be men who will realize the greater benefit. 

The advantage decreases as the “fitness of the drug-resistant 

strains and microbicide efficacy (for women) increases.” 

The Nerenberg Lecture is named after the late Morton 

(Paddy) Nerenberg, a much-loved professor and researcher 

born on 17 March-- hence his nickname. He was a 

Professor at Western for more than a quarter century, 

and a founding member of the Department of Applied 

Mathematics there. Nerenberg was a successful researcher 

and accomplished teacher; he believed in the unity of 

knowledge, that scientific and mathematical ideas belong 

46 

to everyone, and that they are of human importance. He 

regretted that they had become inaccessible to so many, and 

anticipated serious consequences from it. The series honors 

his appreciation for the democracy of ideas. He died in 1993 

at the age of 57. He is survived by his children Albert, Ben, 

and Simone. 

Mitchell Zimmer 

SyMPOSIUM HONOURING NEW FELLOWS OF THE 

ROyAL SOCIETy OF CANADA 


Every year, Fields presents a half-day symposium to 

celebrate the election of new fellows in the mathematical 

sciences at the Royal Society of Canada. The sequence of 

three talks forms one of our most spontaneous events: 

planning does not begin until the announcement of new 

fellows in early summer. And since there are not always 

three new fellows in the mathematical sciences, we often 

have the opportunity to augment the mathematics talks 

with presentations in related disciplines, or with lectures by 

people whose celebrated work uses mathematics in interesting 

ways. We have in the past featured speakers from areas 

as diverse as computer science, geomatics and zoology. 

But this was a banner year for mathematics at the Royal 

Society of Canada. Three distinguished mathematicians 

have been recognized by the Royal Society: David Brydges, 

Walter Craig and Lisa Jeffrey. Not only are they all well 

known to the community, they are well known to Fields. 

new Fellows walter Craig and David Brydges with 

Barbara Keyfitz

All three have served on our Scientific Advisory Panel (one 

currently) and two of the three have organized programs 

here. Perhaps it is a tribute to the rising importance of 

mathematics in all of science that we could not this year 

invite every inductee whose contributions have significant 

mathematical content. Through the symposium, Fields 

offers recognition and congratulations to all of them. 

The first speaker at this year’s symposium, held at Fields 

on March 25, 2008, was David Brydges. David, who 

holds a Canada Research Chair in Mathematical Physics 

at UBC, talked on “Statistical Mechanics and Gaussian 

Integrals.” The talk shed light on some of the mathematical 

foundations of quantum field theory, beginning with the 

appearance of universality in the passage from random 

walks to Brownian motion, and ending with the relation 

between supersymmetry, loops (or their opposite, selfavoiding 

walks) and vacuum energy. David’s talk prepared 

the way for the second speaker, Lisa Jeffrey. 

Lisa’s talk, on “Flat Connections on Riemann Surfaces”, 

began with a lucid explanation of how algebraic quantities 

can be used to describe a surface. Then moduli spaces 

(topological spaces) are associated with these surfaces. 

This definition provided a springboard for the introduction 

of gauge theory, and Yang-Mills theory. That moduli 

spaces have a symplectic structure was first exploited by 

Atiyah and Bott. The space of flat connections on the 

surface plays a special role, because it is mapped to itself by 

gauge transformations. In 1991, Witten gave formulas for 

intersection numbers in the cohomology of moduli spaces. 

Using the theory of moduli spaces, Jeffrey and Kirwan were 

able to provide a rigourous mathematical proof of Witten’s 

formulas. On her last slide, Lisa produced a “dictionary” 

that translates between mathematicians’ and physicists’ 

terminology for the objects of quantum field theory. 

Walter Craig, Canada Research Chair at McMaster, was the 

third speaker. His talk, “Bounds on Kolmogorov spectra 

for the Navier-Stokes equations”, based on joint work with 

Andrei Biryuk, gave a new estimate for weak solutions 

(in the Leray sense) of the Navier-Stokes equations. This 

estimate turns out to be inconsistent with the celebrated 

Kolmogorov scaling law for homogeneous isotropic turbulence 

outside of a range of frequencies. Consequently, one 

gets new bounds on the inertial range for turbulence. 

So, by the end of the afternoon, the audience had learned 

that the mathematicians honoured by the Royal Society of 

Canada have made contributions, not only to fundamental 

mathematics, but to statistical mechanics, quantum field 


theory, and turbulence. That was worth a toast, which we 

celebrated at a reception and a very cheerful dinner. 

Speakers: 

David Brydges (UBC) 

Statistical Mechanics and Gaussian Integrals 

Lisa Jeffrey (Toronto) 

Flat Connections on Riemann Surfaces 

Walter Craig (McMaster) 

Bounds on Kolmogorov spectra for the Navier-Stokes equations 


FIELDS-CARLETON DISTINGUISHED LECTURE SERIES 

Philippe Flajolet (INRIA) 

Counting with probabilities; Analytic combinatorics: A calculus 

of discrete structures 


Held at Carleton University 

The Fields-Carleton Distinguished Lecture Series for 2008 

was delivered by Philippe Flajolet of INRIA (Rocquencourt, 

France). The two lectures were related to analytic combinatorics. 

Previous speakers of this yearly series were Donald 

Saari in 2006 and Jerry Marsden last year. 

Flajolet is a former student of the Ecole Polytechnique in 

Paris, and completed his Ph.D. in Computer Science in 1977 

and his doctorate of state in 1979 at the University of Paris 

VII. He is currently a research director (senior research 

scientist) at INRIA. He was appointed a corresponding 

member of the French Academy of Sciences in 1994, 

becoming a full member in 2003, and was awarded the 

philippe Flajolet 

47


Silver Medal of the CNRS in 2004. He also belongs to the 

Academia Europaea, and has been a member of the editorial 

committees of the most prestigious journals and of the 

program committees of the most important conferences in 

his field. 

Flajolet has an impressive career with about 200 publications, 

many of which have been very influential. A 

summary of his research up to 1998 can be found in the 

article Philippe Flajolet’s research in Combinatorics and 

Analysis of Algorithms (Algorithmica 22 (1998), 366-387) 

by H. Prodinger and W. Szpankowski. Most of Flajolet’s 

research work has been dedicated to generic methods for 

the analysis of algorithms, with the main focus on averagecase 

analysis of algorithms and, more generally, the effect 

of randomness in algorithms. He is a pioneer and leader of 

the theory of Analytic Combinatorics that provides generic 

methods involving combinatorics (enumeration, generating 

functions), classical analysis (asymptotics, complex 

analysis) and probability (moments, limiting distributions) 

for the analysis of algorithms. Among his many contributions 

in this area is the book Analytic Combinatorics (joint 

with Robert Sedgewick of Princeton) to be published by 

Cambridge University Press this year – available online at 

Flajolet’s homepage and already considered the most fundamental 

book on this area. 

The main topics of Philippe Flajolet’s two talks at Carleton 

were related to analytic combinatorics. The first talk, 

Counting with probabilities, was designed for the general 

public. Many recent algorithms have focused on extracting 

information from very large data sets, so large that 

they cannot be stored in a computer. These algorithms are 

random in nature and applicable in areas such as traffic 

monitoring in networks, database query optimization, 

and data mining. The type of information one would like 

to gather – with a small probability of error – are the total 

number of data entries, cardinality (the number of distinct 

entries), frequency moments, unbiased samples, and so 

on. The design and analysis of these algorithms involve a 

variety of methods from discrete mathematics, complex 

and asymptotic analysis, and probability theory, that make 

them, as Flajolet showed, particularly interesting for analytic 

combinatorics. 

The second talk Analytic combinatorics: A calculus of discrete 

structures, gave a thorough description of the mathematics 

behind analytic combinatorics. The subject aims to predict 

properties of large structured combinatorial configurations 

through an approach based extensively on analytic methods. 

48 

Generating functions are the central objects of study in 

this theory. A collection of theorems provides a systematic 

translation mechanism between combinatorial constructions 

and operations on generating functions. Usually the 

extraction of coefficient information from these generating 

functions is difficult. As a consequence, the second step 

involves obtaining asymptotic information –the most 

common techniques for which are Flajolet and Odlyzko’s 

singularity analysis method and the saddle point method. 

Finally, the typical behaviour of parameters (moments 

and limiting distributions) of random discrete structures 

is studied. This involves, in general, central limits and 

deviation theorems, as well as multivariate generating functions. 

As a typical example of this procedure one obtains 

a normal distribution for the number of cycles in the cycle 

decomposition of random permutations. Many more concrete 

examples were given at the talk. 

As was clear to the audience, Philippe Flajolet is not only 

an authority in the analysis of algorithms but also a master 

of exposition. His talks at Carleton combined topics from 

several mathematical areas with a practical, applied orientation, 

which made them greatly enjoyable to those who 

attended the lectures. 

Daniel Panario 

FIELDS 2008 Annual General Meeting 

June 26, 2008 

In keeping with tradition, Fields began the AGM with a 

luncheon for representatives of the Principal Sponsoring 

Universities and Affiliate Universities. There were eighteen 

guests and the Fields Directorate. There was a discussion of 

plans to take advantage of the NSERC CREATE program 

as a replacement for Grad Day. An outline of an expanded 

postdoctoral program was also presented to the participants 

and there was a lively discussion of its merits. Barbara 

Keyfitz also proposed a Research Immersion program 

explaining that the idea initially came out of a meeting at 

BIRS. It is designed to help women who have taken time 

off to have children, or for other reasons, to get back into 

research. 

This year’s AGM colloquium featured Pit-Man Wong 

talking about the upcoming thematic program Arithmetic 

Geometry, Hyperbolic Geometry and Related Topics. 

The AGM itself well attended. It was chaired by John 

Gardner, who welcomed all members. He informed the 

meeting of the status of the director search and remarked

on the number of qualified and interested candidates. He 

also spoke of the government support, referring to financial 

reports and announcing our new funding. Turning to 

fundraising he noted that Fields has received significant 

gifts in the past year. George Elliott’s gift allowed Fields to 

augment a thematic program and another gift from him 

has increased participation in the Institute. Ron Dembo 

and David Rudd both provided matching funding for our 

annual drive. 

The Director’s report highlighted the increase in MTCU 

funding, it being a sign of the value of Fields to the 

province. She also spoke of the thematic programs at 

the Institute. There are a number of thematic programs 

approved for the next 4 years, but no proposals in the pipeline. 

She asked participants to keep an eye out generally, 

and more specifically for an interdisciplinary program for 

summer 2009. The Director explained that the General Scientific 

Activities at Fields are increasing in size and number 

and she highlighted Allan Borodin’s CRM-Fields-PIMS 

prize and lecture. She also reported that RMC and Trent 

are now affiliates, and that Fields continues to enjoy great 

relations with U of T. She offered thanks to departing BOD 

members. 

The financial report showed an operating deficit of over 

$150k. Juris Steprāns reminded the meeting that there was 

a supplementary budget previously presented to the BOD 

predicting a deficit of $200k. More money was spent this 

year on GSA and updated AV equipment. 

This year, six new Fields Institute Fellows were announced: 

Allan Borodin, Jennifer Chayes, Rick Jardine, Angus 

Macintyre, Cameron Stewart, and Karen Uhlenbeck. Fields 

congratulates the new Fellows and thanks them for their 

service to Fields and to mathematics. 

As its final official action of the meeting, a quorum of 

members of the corporation elected the Board of Directors 

for 2008-2009. Three new members were welcomed to the 

Board: Gregory Margulis, Ram Murty and Graham Weir. 

The AGM was followed by a brief meeting of the new 

Board of Directors, to re-elect John Gardner as chair and 

Philip Siller as deputy chair, and to form committees for 

2008-2009. 

The day ended with a banquet for Members of the Corporation, 

Fields staff and guests. This year’s dinner, at 

the University of Toronto Faculty Club, was particularly 

lively, with delicious food, good conversation, and three 

talks. Barbara Keyfitz discussed her views on the role of 


mathematics institutes, Paul Young shared his vision of the 

Fields Institute within the university and Janet Mason commented 

on the value of the Institute to the province. 


AGM Lecture 

Pit-Mann Wong (Notre Dame) 

Arithmetic Geometry and Hyperbolic Geometry 

June 26, 2008 

To many mathematicians, the two subjects of Pit-Mann 

Wong’s talk appear to have little relation to each other 

although they are both “geometry”. But it has become 

increasingly clear in recent years, as Wong convincingly 

argued in his lecture, that there is in fact a deep connection 

between them which is not yet completely understood. One 

of the main goals of this fall’s program is to investigate and 

further clarify the connections between these two geometries 

by bringing together many of the experts in each field. 

In some ways, the arithmetic geometry in question goes 

back to the 19 th century when Liouville proved in 1844 

that transcendental numbers exist, followed not long after 

(1873) by Cantor’s startling (and controversial) proof of 

their ubiquity, using cardinal numbers. The “theory” of 

transcendental numbers was given even more prominence 

through Hilbert’s 7 th problem – if α is an algebraic number 

pit-Mann wong 

49


different from 0 and 1 and β is algebraic and irrational, is 

α β transcendental? This was solved affirmatively by A.O. 

Gelfond and Th. Schneider independently in 1934, and is 

now known as the Gelfond-Schneider theorem. 

Shortly thereafter, C.L. Siegel initiated the use of function 

theory in the subject by considering a transcendental function 

f: C → C U {} and investigating the cardinality of the 

set f -1 (K) where K is an algebraic number field. He showed 

that for many transcendental functions, f -1 (K) is finite – in 

fact he gave an explicit upper bound for its cardinality. 

Siegel’s work was reformulated and extended by Serge Lang, 

and the most general form at this time is E. Bombieri’s 

theorem (1970), proved using deep results from analysis – 

viz. the method of L 2 -estimates of Hörmander: 

Let f = (f 1 , f 2 ,… f n ): C m → C n be a map with the f i meromorphic 

such that the field K(f 1 , f 2 ,… f n ) has transcendence 

degree at least m+1 and the partial derivatives ∂/∂z i take K(f 1 , 

f 2 ,… f n ) into itself, for all i. Then f -1 (K) is contained in an 

algebraic set P(z 1 ,z 2 ,…,z m ) = 0 (where P is a nonzero polynomial 

in C[z 1 , z 2 ,… z n ], of explicitly bounded degree). 

Lang had proved this for m = 1 – in which case f -1 (K) is of 

course finite. 

Wong continued at this point with an example showing 

the relationship between Diophantine equations and Diophantine 

approximation, using the example x 3 – 2y 3 = 1. 

The Diophantine approximation problem relevant to this 

Diophantine equation is 

50 

|x/y – 2 1/3 | ≤ C/|y| 3 

where x and y are integers and C is a positive constant. 

“Roth’s Theorem”, 

Let r be an irrational algebraic number. Then for any ε > 0, 

there exists a constant C > 0 such that there are only finitely 

many rational numbers x/y satisfying 

|x/y –r| ≤ C/|y| 2+ε 

when applied in the foregoing case (when r = 2 1/3 ) shows 

that x 3 – 2y 3 = 1 has only finitely many integral solutions. 

A. Baker later found an effective form of Roth’s Theorem, 

providing an upper bound for |y| in solutions (x,y) and 

enabling all integral solutions to be found. 

The following “logarithmic” form of Roth’s Theorem 

Then for any ε > 0, 

|x/y – r| 

(x/y) 

holds for all but finitely many rational numbers x/y where 

h(x/y) = log |y| is the “height” of x/y. 

is useful for comparison to the Second Main Theorem in 

Nevanlinna Theory which is stated later. 

A crucial step, as far as the theme of this fall’s program is 

concerned, was the extension of Roth’s Theorem to higher 

dimension (multiple variables, simultaneous Diophantine 

approximation) by W. Schmidt, now known as Schmidt’s 

Subspace Theorem: 

Let L 0 , L 1 ,…, L n be homogeneous linear forms in x 1 ,…, x n 

with coefficients which are algebraic and linearly independent 

over Q. Then for any ε< 0, there exists a finite number of 

hyperplanes H 1 ,…, H N in P(Q) n and a constant C > 0 such 

that all integer solutions of the inequality 

|L0 (x/|x|)….Ln (x/|x|)| ≤ C/|x| n+1+ ε 

are contained in the union of the H i . 

Again the logarithmic version of this inequality is more 

germane to the subject of the lecture: the inequality 

n 

∑ 

i= 

0 

holds for all integral vectors x outside the union of the H i . 

At this point, Wong turned his attention to function theory 

– more precisely the theory of holomorphic functions. Here 

the interest is also in the solution of Diophantine equations 

but this time by functional solutions. For example x = sin θ, 

y = cos θ is a solution to 

x 2 + y 2 = 1. 

It can also be shown, for example, that the only holomorphic 

solutions to 

are constants. 

log 

| 

L i 

1 

( x) 

| 

( n + 1+ 

ε ) h( 

x) 

+ O( 

1) 

x 3 – 2y 3 = 1 

Hyperbolic geometry is the other subject of interest to the 

thematic program: 

Definition. A complex space X is hyperbolic if every holomorphic 

map f: C → X is constant. 

For example, the following spaces are hyperbolic: 

≤ 

L \ {3 distinct points of L} where L is a (projective) rational 

curve (a curve of genus 0),

E \ {one point of E} where E is an elliptic curve (a curve of 

genus 1) 

Every projective (or compact ) curve of genus ≥ 2. 

There are several proofs that these spaces are hyperbolic. 

The one of most interest to this program is the Second 

Main Theorem (SMT) of Nevanlinna Theory: 

Let f: C → C be a nonalgebraic meromorphic function. Then 

for any q distinct points a 1 , …, a q in P 1 , 

where the estimate holds for all r outside an exceptional set of 

finite Lebesgue measure. 

The left side is known as the proximity function and T f (r) 

is called the characteristic function. It is the analogue of the 

height function of number theory. 

The SMT can be generalized to higher dimension: 

Let L 1 ,…,L q be q hyperplanes in general position in P n . Then 

for any linearly nondegenerate holomorphic map f: C → P n , 

where the estimate holds for all r outside an exceptional set of 

finite Lebesgue measure. 

This is the analogue of Schmidt’s Subspace Theorem. Its 

resemblance to that theorem is very striking, and suggests 

a deep relationship between Diophantine geometry 

and hyperbolic geometry. In fact P. Vojta introduced a 

“dictionary” which allows one to translate an assertion in 

Nevanlinna Theory to one in Diophantine approximation, 

and vice-versa. At this point this correspondence is an ad 

hoc procedure – no-one has yet been able to show that the 

process is really legitimate. 

Even more striking is the fact that many proofs can be 

translated from one theory to the other via the principle 

that any statement in hyperbolic geometry provable using 

only the SMT, when translated into Diophantine geometry, 

can be proved using only Schmidt’s Subspace Theorem, and 

conversely. Some examples: 


1. It was discovered that the SMT of Nevanlinna implies 

that the space 

P n \ {2n + 1 hyperplanes in general position} 

is hyperbolic. It was observed that the proof carries over to 

Diophantine geometry and yields the higher dimensional 

analogue of Siegel’s theorem in dimension 1. Namely the 

complement of 2n+1 hyperplanes, defined over Q, in P n 

admits only finitely many integral points. 

2. P. Corvaja and U. Zannier extended Schmidt’s Subspace 

Theorem for hyperplanes to the case of hypersurfaces of 

degree d. M. Ru translated the proof to prove the SMT for 

hypersurfaces. 

There are also other results of hyperbolic geometry such as 

Bloch’s Theorem on subvarieties of Abelian varieties and 

Lang’s conjecture on an ample divisor of an Abelian variety, 

proved by Y.-T. Siu and S.-K Yeung, which have been proved 

“directly” (in this case properties of elliptic curves by Faltings) 

but have not yet been proved by “translation.” 

There are many open and intriguing problems in this 

marriage between Diophantine geometry and hyperbolic 

geometry. For example there is a well-developed p-adic 

Nevanlinna theory and p-adic hyperbolic geometry but 

their relationship to p-adic Diophantine geometry remains 

relatively unexplored. Similarly there is a theory of p-adic 

dynamics but again its relationship to complex dynamics 

has not yet received much attention. 

The organizers of the Fields thematic program on arithmetic 

and hyperbolic geometry hope that progress will be 

made on these and many other problems of this kind. 

Carl Riehm 

51

The National Program on Complex Data Structures 

The National Program on Complex Data Structures (NPCDS) 

The National Program on Complex Data Structures ended 

an extraordinarily successful 5 years on April 30, 2008. It 

is in the process of being transformed into the National 

Institute for Complex Data Structures, with primary funding 

from NSERC’s Major Resource Support Grants (MRS) 

program. 

To this end a proposal was submitted in October, 2007. 

Major features of the MRS proposal for the new Institute 

were a continuation and expansion of the collaborative 

research projects of NPCDS, a large increase in support 

for postdoctoral fellows associated with the projects, and 

new international initiatives with Statistical Sciences 

Institutes in the US and Europe. In January, 2008 we held 

an inspiring site visit at the University of Toronto for an 

internationally renowned team of reviewers. Leadership 

and scientific presentations were exciting and well focused, 

and the case for the NICDS approach to collaboration with 

scientists and statisticians seemed as strong as it could be. 

To our great dismay and surprise, this excitement did not 

survive the reviewing process, and we appealed the negative 

decision of the MRS Committee. The appeal was successful 

in obtaining one year of funding for NICDS, but most 

importantly this funding enabled the establishment of 

NICDS as an entity, which gave us the means to continue to 

leverage NSERC’s investment and to continue our work as 

a voice for interdisciplinary statistics and science. We have 

formed a partnership with Accelerate Canada to enhance 

our internship program, have held a consensus meeting 

with the Canadian Institutes for Health Research to outline 

research areas of mutual interest and strategies for raising 

the level of collaborative quantitative research and training 

in the health sciences, and have established sponsorship 

agreements with several Departments of Statistics across 

Canada. The writing team of Derek Bingham, Hugh Chipman, 

Charmaine Dean, Christian Léger, Nancy Reid and 

James Stafford are hard at work preparing a re-application 

to be submitted this fall. The re-application process is 

documented on our wiki site, www.nicdsreapplication. 

pbwiki.com/ 

In the meantime, our projects continue their research and 

training efforts. The project on Statistical Innovation for 

the Analysis of Complex Data in Medical and Health Science 

started in September, 2007, and held a short course 

and a workshop at PIMS in April, 2008. This workshop on 

52 

Methodological Needs and Desires in Public and Population 

Health Research emphasized workshop participation of both 

health researchers and statisticians to foster technology 

transfer of innovative statistical methodology into health 

research applications. The project on Climate Statistics 

in Agriculture held its inaugural workshop in June 2007 

in Regina, and has begun work in earnest on its research 

objectives of developing methods for localized weather 

forecasting, predicting extreme events, and spatial interpolation. 

The project on Forests, Fires, and Stochastic Modelling 

held a workshop at the University of Western Ontario 

in November, 2007 on the mathematical and statistical 

modelling of the spread of biological and physical processes 

in forests. The project on Statistical Methods for Complex 

Survey Data, continues its enormously successful internship 

program by welcoming three new interns to Statistics 

Canada in September, 2007. These and other activities 

strengthen our conviction that model of NICDS and the 

vision it has created for statistics in Canada is innovative 

and exciting, and is the way the discipline will move forward. 

Nancy Reid

Workshops and Conferences 

Workshop on Perspectives for Future Directions in 

Computational and Mathematical Neuroscience 

July 7, 2007 

Organizers: Sue Ann Campbell (Waterloo), Mary Pugh 

(Toronto), Frances Skinner (Toronto Western Research 

Institute), Rich Zemel (Toronto) 

July 7 was an ideal date for the workshop – it was the day 

before the sixteenth annual Computational Neuroscience 

meeting, which also took place in Toronto (first time in 

Canada). Frances Skinner was the local organizer of that 

meeting, allowing us to piggy-back on the big meeting in 

terms of both speakers and participants. 

Computational Neuroscience seeks to understand how 

the brain and nervous system compute. This is a highly 

interdisciplinary field thus making it somewhat difficult to 

navigate and to understand where and how one might be 

able to fit in. The goal of our workshop was to obtain perspectives 

for future directions in the field. The workshop 

was a somewhat unorthodox one; it was designed to stimulate 

discussion and networking, rather than being primarily 

a venue for research talks. 

The morning part of the workshop featured six half-hour 

talks by well-established practitioners in the area: Sue 

Becker, Ron Calabrese, Doug Crawford, André Longtin, Jon 

Rubin, and Hugh Wilson. They were chosen to represent a 

wide range of research views, from the top-down view of 

theoretical neuroscience to the hard reality of experimental 

neuroscience, and the range of methodologies in between 

(biophysics, data modelling, deterministic models, models 

with noise). 

In addition to describing their own research highlights in 

the field, the speakers were asked to provide their opinions 

and insights on how they defined the field, what they 

thought were critical considerations for someone wanting 

to enter the field today, what they thought were ideal types 

of training, and what they would suggest for changes and 

directions in the field. 

These short talks were followed by a quick lunch and then a 

series of afternoon discussions. We divided the six speakers 

up among the two seminar rooms on the second floor and 

the library on the third floor. Participants broke up into 

three groups, with each group going off to visit two of the 

morning’s speakers. After a discussion of thirty to forty 

minutes, the groups rotated to the next pair of speakers and 


so on. In this way, the participants were able to have group 

discussions with the speakers and with one another. After 

these discussions, we all joined up again to compare notes. 

Some of the results of the talks and group discussions are 

as follows. It was universally felt that more synergy and 

better communication between theory and experiment are 

needed, as well as mutual appreciation between experimentalists 

for the work involved in performing experiments and 

theoreticians for modelling and analysis. Significant time 

and effort are required to develop cross-disciplinary relationships. 

As a result, having good mentorship should be of 

top priority for someone entering the field. Injecting more 

flexibility into graduate programs as well as having “translation” 

type shared courses between theory and experiment 

would be useful. 

Aside from organizers and speakers, there were over 

sixty-five participants that included undergraduates (~6), 

graduate students (~25), postdocs (~10), faculty (~15), 

program officers from the National Science Foundation 

and National Institutes of Health, and several others (~15). 

We were delighted with the large number of undergraduate 

and graduate students, and we were personally thanked by 

several participants who found the discussions to be invaluable. 


Sue Becker (McMaster) 

Understanding hippocampal-cortical interactions in memory, 

sleep and dreaming: linking computational theory to largescale 

brain dynamics 

Ron Calabrese (Emory) 

A future for experimental models? 

Doug Crawford (York) 

Levels of theory in sensorimotor neuroscience 

André Longtin (Ottawa) 

Active sensory dynamics 

Jonathan Rubin (Pittsburgh) 

From the Evans function to deep brain stimulation and back 

Hugh Wilson (York) 

Binocular rivalry: waves, feedback, hysteresis, and perceptual 

memory 

Sue Ann Campbell 

53


The 18th Annual Symposium on Combinatorial Pattern 

Matching 

July 9–11, 2007 


Organizers: Bin Ma, Roberto Solis-Oba, Kaizhong Zhang 

(Western) 

Combinatorial pattern matching deals with the fundamental 

problem of searching for given patterns in linear and 

non-linear structures such as strings, trees, and graphs. 

Research in this area has a large and diverse number of 

applications including information retrieval, data compression, 

and computational biology. The Symposium provided 

a significant mechanism for disseminating some of the 

most notable advances in this exciting field. 

The instalment of the symposium took place at Western’s 

beautiful London campus. It was attended by seventy-seven 

scientists from Australia, Canada, Chile, China, Denmark, 

France, Finland, Germany, Hong Kong, Italy, Israel, Japan, 

Korea, Poland, Russia, the United Kingdom, and the USA, 

and a total of thirty-two papers were presented. These 

25-minute talks addressed important problems from computational 

biology, data compression, pattern analysis, and 

algorithmic techniques. 

Of special mention were the two invited talks, and the 

open-problem session at the end of the symposium which 

was organized to cover the absence of an invited speaker 

who had run into travel difficulties. The first invited talk 

was given by Tao Jiang, who spoke about new approaches 

to the assignment of orthologous genes between genomes 

(a fundamental problem in genomics). The second was of 

a broader scope: Muthu Muthukrishnan gave an overview 

of classical problems that can be solved with suffix trees 

and posed what he believes are some of the most important 

open problems in this area. The open-problem session 

chaired by Ian Munro prompted a number of participants 

to pose a variety of interesting and challenging problems 

that stimulated vigorous on-the-spot discussions. 

The CPM 2007 best paper prize was awarded to Shay 

Mozes, Oren Weimann, and Michal Ziv-Ukelson for Speeding 

up HMM decoding and training by exploiting sequence 

repetitions. Mozes attended the conference and accepted the 

award. 

On the second day of the event, the participants were 

treated to a trip to the Stratford Festival, where they were 

given the choice of seeing a Shakespeare play, either Othello 

or The Merchant of Venice. 

54 

Invited Speakers: (in alphabetical order) 

Tao Jiang (Riverside) 

A combinatorial approach to genome-wide ortholog assignment: 

beyond sequence similarity search 

Muthu Muthukrishnan (Rutgers and Google) 

Stringology: some classic and some modern problems 

Roberto Solis-Oba 

Fields Institute Summer Workshop on Environmetrics 

July 17–19, 2007 

Held at the University of Waterloo 

Organizers: Grace Chiu (Waterloo), Abdel El-Shaarawi 

(Environment Canada), Román Viveros (McMaster) 

The aims set out by the workshop organizers were: to raise 

awareness and interest of environmental scientists and 

statisticians–particularly those from North America–about 

environmetrics; to join forces and integrate the expertise of 

the two groups; and to generate interest about and explore 

the creation of a graduate program in environmetrics in 

Central-Eastern Canada. 

As all the conference objectives were fully met, we were very 

pleased with the outcome. 

The workshop was attended by twenty-five statisticians, 

biologists, and ecologists from academia, fifteen leading 

scientists from government agencies and research centres, 

five scientists from the private sector, and forty graduate 

students. Registrants came from Canada, the United States, 

the Middle East, and Africa. 

Several presentations on the first day focused on raising 

the awareness of environmental statistics. They considered 

why and how statistics is integrated into environmental 

research, and discussed a rich variety of popular statistical 

methodologies used in environmental research. 

Talks on the following day focused on a number of challenges 

encountered in doing environmental research. 

Presentations ranged widely over issues such as obstacles 

that hinder work to questions of funding. The day concluded 

with two multimedia shows on emerging, exciting, 

research areas in environmetrics. 

Day three addressed the desirability, feasibility, and possible 

structure of a graduate program in environmetrics. The 

audience was enthusiastic about the initiative; their support 

was greatest for the model which situated the program in a 

university with strong statistics and environmental sciences

programs, and which included collaboration with scientists 

from other universities and from government agencies and 

research centres. 

It was a diverse audience. It was refreshing for the organizers 

to witness the high interest shown by students as well 

as the influential roles played by a number of participants 

including the President of the International Environmetrics 

Society and two editors of leading international journals on 

environmetrics. Interaction between speakers and audience 

occurred throughout the workshop. 

We gratefully acknowledge the support provided by the 

Fields Institute, our main sponsor, and by the Department 

of Statistics and Actuarial Science and the Faculty of Mathematics 

at the University of Waterloo, by MITACS, and by 

the Statistical Society of Canada. Their support allowed us 

to avoid registration fees for participants and provide partial 

support for travel and accommodation for students and 

speakers in addition to coffee breaks, a reception, registration, 

and advertising of the workshop. 

Invited Panelists: (as listed on program itinerary) 

Michael Dowd 

The integration of statistics into environmental prediction 

research 

Abdel El-Shaarawi (Environment Canada) 

Environmental problems: Identification, assessment and 

management 

David Brillinger (Berkeley) 

Probabilistic risk modeling at the wildland-urban interface: 

the 2003 Cedar Fire, III 

environmetrics workshop participants 


Mark Buehner (Environment Canada) 

Data assimilation for numerical weather prediction: 

Estimation and modelling of the covariances of short-term 

forecast error 

David Stanford (Western) 

Analyzing extra fire-fighting costs in the province of Ontario 

John Braun (Western) 

Stochastically modelling forest fire spread 

Stephen Murphy (Waterloo) 

Issues in using environmetrics in ecosystem research 

Maren Oelbermann (Waterloo) 

How a soil scientist approaches statistics 

Jonathan Grant (Dalhousie) 

Applied statistics in ecology and biological oceanography 

Richard Routledge (SFU) 

Impediments to environmental research 

Grace Chiu (Waterloo) 

Where’s the statistician? A collage of high profile environmental 

issues 

Richard Routledge (SFU) 

Rivers inlet ecosystem study: a case study in ecosystem 

research 

Grace Chiu 

55


Workshops on Symbolic-Numeric Computation (SNC 

2007) and Parallel Symbolic Computation (Pasco 2007) 

July 25–27 and July 27–28, 2007 


Organizers: Stephen Watt, Marc Moreno Maza, Oleg 

Golubitsky, Eric Schost, Francois Lemaire, Meg Borthwick 

(Western) 

These workshops featured a host of internationally 

renowned invited speakers and full programs of contributed 

research papers. Symbolic-Numeric Computation 

focused on hybrid symbolic/numeric algorithms for problems 

in a range of areas, including linear algebra, algebraic 

geometry and differential algebra. Algorithms that combine 

ideas from symbolic and numeric computation have been 

of increasing interest over the past decade. An example of a 

basic problem in this area is: Given two polynomials 

p, q in R[x] and a radius ε, do there exist polynomials 

p + ∆p and q + ∆q, with non-trivial gcd for ||∆p||, ||∆q|| < ε? 

If so, how may they be characterized and how may they be 

computed? Not only do the usual algorithms of computer 

algebra break down when applied to such inexact values, 

but the analytic setting itself allows many new questions 

to be asked. This, together with the growing demand for 

speed, accuracy and reliability in mathematical computing, 

has accelerated the process of blurring the distinction 

between two areas of research that were previously quite 

separate. The SNC workhsop at Western followed earlier 

meetings in Sophia Antipolis (France) and Xi’an (China) 

and featured André Galligo, Erich Kaltofen, Nick Trefethen, 

Charles Wampler and Lihong Zhi as invited speakers. 

To allow common problems to be discussed, the last day 

of the SNC workshop overlapped with the first day of the 

workshop on Parallel Symbolic Computation. The ubiquity 

of parallel architectures, from symmetric multiprocessing 

on high-performance computers to multi-core laptops, 

has led to a new quest for mathematical algorithms and 

software capable of exploiting these computing resources. 

Symbolic computation offers exciting, but highly complex, 

challenges to scientists aiming to contribute to this quest. 

The goal of the PASCO workshop was to stimulate the 

development of parallel algorithms and software for achieving 

high performance in symbolic computation at all scales 

– from grids to personal computers. Earlier meetings in this 

series had been held in Linz (Austria) and Maui (USA). The 

invited speakers of PASCO included Mike Bauer, Matteo 

Frigo, Thierry Gautier and Katherine Yellick. Keith Geddes 

56 

and Anthony Kennedy presented invited talks common to 

the two workshops. 

As well as support from Fields, the two conferences received 

support from MITACS, Research Western, the Ontario 

Research Centre for Computer Algebra, Maplesoft and 

SharcNet. 


André Galligo (Nice-Sophia Antipolis) 

Approximate Bivariate Factorization: a Geometric Viewpoint 

Keith Geddes (Waterloo) 

Symbolic-Numeric Reflections: One Person’s 35-year Perspective 

Erich Kaltofen (North Carolina) 

On Probabilistic Analysis of Randomization in Hybrid 

Symbolic-Numeric Algorithms 

Anthony Kennedy (Edinburgh) 

Automating Renormalization of Quantum Field Theories 

Nick Trefethen (Oxford) 

Computing Numerically with Functions instead of Numbers 

Charles Wampler (General Motors) 

Numerical Algebraic Geometry and Kinematics 

Lihong Zhi (Chinese Academy of Sciences) 

Numerical Optimization in Hybrid Symbolic-numeric Computation 

Stephen Watt 

International Symposium for Symbolic and Algebraic 

Computation (ISSAC 2007) 

July 29–August 1, 2007 

Held at University of Waterloo 

Organizers: General Chair, Dongming Wang (CNRS); 

Program Chair, Bernard Mourrain (INRIA – Sophia Antipolis); 

Posters Chair, Gladimir Gerdt (Joint Institute for 

Nuclear Research, Dubna, Russia); Local Organizers: Keith 

Geddes, Mark Giesbrecht, George Labahn, Arne Storjohann 

(Waterloo) 

The International Symposium for Symbolic and Algebraic 

Computation 2007, held this year at the University of 

Waterloo, is the premier international conference in computer 

algebra. It attracted nearly two hundred computer 

algebra researchers from around the world, the largest 

attendance in the past fifteen years. Held in 2006 in Genoa, 

Italy, it is planned in 2008 for Linz, Austria, and in 2009 for 

Seoul, Korea.

This year’s event consisted of a day of tutorials followed by 

three days of talks, software demonstrations, and poster 

sessions. For the first time in ten years there were parallel 

sessions for the contributed talks. This ensured that there 

was plenty of time available for discussion among participants 

and for viewing poster presentations. 

The first day consisted of three diverse tutorials on differential 

equations, algebraic geometry, and symbolic linear 

algebra. Tutorial attendance was also at record levels, with 

some of the tutorials having more than seventy participants. 

The day began with the tutorial by Fritz Schwarz, 

titled Loewy decomposition of linear differential equations. 

The goal was to give students and researchers an introduction 

to techniques for working with rings of differential 

operators (ordinary and partial), their ideals and their 

decompositions. Tools for such techniques come from differential 

algebra and factorization of operators. 

The second tutorial, by David Cox, was on the topic of 

Gröbner bases, a central tool used for working with multivariate 

polynomial systems and polynomial ideals. The 

tutorial gave a short, but detailed, introduction to Gröbner 

bases, including concepts such as monomial orderings 

and consistency theorems. This was followed by information 

about the use of Gröbner bases in the geometry of 

elimination and then a discussion of recent developments 

and applications of these polynomial ideal bases. This 

tutorial was particularly well received, as Cox is the author 

(with Little and O’Shea) of the book Ideals, Varieties and 

Algorithms, which is recognized as the introductory yet fundamental 

textbook in computational algebraic geometry. 

The last tutorial, by Gilles Villard, presented recent progress 

in the area of Symbolic Linear Algebra. Of particular 

note was information presented about the improvement 

of complexity estimates for fundamental problems such as 

linear system solution, determinant, inversion, and computation 

of canonical forms. Villard showed the way in which 

these improvements could be used in the construction of 

new, effective algorithms for use in high performance linear 

algebra libraries. Some of the results themselves were illustrated 

by showing computations done in the LinBox, a C++ 

high performance linear algebra library. The algorithmic 

improvements were available by running inside a Maple 

computer algebra system. 

The conference had three invited talks, the intent being to 

cover areas important for computational mathematics that 

come from both inside and outside the main recognized 

areas of computer algebra. The first talk was presented by 

William (Velvel) Kahan, a Canadian who was awarded a 


Turing award in 1989 for his work on IEEE arithmetic. (The 

Turing award is to computer science what the Fields Medal 

is to mathematics.) In his talk, Kahan emphasized the need 

for careful error analysis in numerical computation but also 

noted the lack of available expertise available to do such 

tasks. He pointed to the disappearance of floating point 

error analysis in today’s undergraduate and graduate curriculums 

as the main cause of this shortage of expertise. He 

challenged compiler researchers in programming languages 

and compilers to provide tools that would help with the 

analysis of floating point computations. 

The second invited talk by Jean Bernard Lasserre discussed 

the problem of numerical computation of the real radical of 

a system of polynomial equations. There are several symbolic 

approaches to computing the real solutions of such 

systems. The interesting and original approach presented by 

Lasserre resorted to techniques developed in the realm of 

algebraic optimization. In this case, nonlinear optimization 

on a convex set is reduced to semi-definite programming 

through representation theorems in real algebraic geometry, 

involving sums of squares or moment matrices. These 

are then combined with relaxation techniques introduced 

by Lasserre. The talk was an excellent illustration of the 

interconnection of algebra and computations, even in a 

numerical setting. 

The final invited talk was given by Hoon Hong on the topic 

of subresultants and their generalizations. Subresultants 

are standard tools used in computer algebra for working 

with greatest common divisors of polynomials or roots of 

polynomials. They are typically defined by an expression 

in the coefficients of the polynomials. Hong illustrated the 

use of this tool and showed his attempts at capturing the 

elegance of their use but with alternate descriptions of the 

polynomials, in particular when they are defined in terms 

of their roots. Work on generalizations to a multivariate 

setting was also presented. 

In addition to the tutorials and invited talks, there were 

fifty research papers presented at the conference. These 

papers were thoroughly refereed (accepted paper had at 

least three reviews). The best paper award was given to 

Hongbo Li (Chinese Academy of Sciences) for A Recipe for 

symbolic geometric computing: long geometric product; the 

best student paper award was presented to Marc Dohm 

(Nice) for his paper on Implicitization of bi-homogeneous 

parametrizations of algebraic surfaces via linear syzygies 

(with Laurent Busé). Both awards are sponsored by ACM/ 

SIGSAM. Another conference talk that should be mentioned 

is Towards the optimal bound for solutions to Rubik’s 

57


Cube by Dan Kunkel and Gene Cooperman, who showed 

that it is always possible to solve the Cubic Rubik puzzle in 

at most twenty-six moves no matter where one starts. The 

procedure, which makes careful use of computing science 

combined with group theory to find all possible successful 

paths, caught the attention of numerous outside press agencies, 

ranging from local newspapers all the way to the BBC. 

Sponsorship for ISSAC 2007 came from the Association 

for Computing Machinery (ACM), the Fields Institute, the 

Faculty of Mathematics at the University of Waterloo, and 

Maplesoft Inc., an industrial sponsor. Local hosts were the 

Symbolic Computation Group in the David R. Cheriton 

School of Computer Science. 

Tutorial Speakers: 

Fritz Schwarz (Fraunhofer Institute) 

Loewy decomposition of linear differential equations 

David Cox (Amherst College) 

Gröbner bases 

Gilles Villard (École Normale Supérieure de Lyon) 

Symbolic linear algebra 

Invited Speakers: 

Hoon Hong (North Carolina State) 

Subresultants in roots 

William Kahan (Berkeley) 

The top of a wish-list for the integration of hardware floatingpoint 

computation into computerized algebra systems 

Jean Bernard Lasserre (CNRS) 

Solving polynomial equations via semi-definite programming 

and linear algebra 

George Labahn 

Ontario Topology Seminar 

July 30–31, 2007 

Organizers: Tony Bahri (Rider College), Lisa Jeffrey 

(Toronto), Paul Selick (Toronto) 

The purpose of this two-day workshop was to highlight 

recent progress in homotopy theory and in geometry. The 

talks were largely subdivided between two main foci of 

interest in the talks. One was homotopy theory and its 

relations with algebraic structures (including Lie groups 

and Lie algebras). The other was geometry, notably including 

gauge theory of moduli spaces of flat connections on 

2-manifolds (both orientable and nonorientable). 

58 

Two speakers (Tom Baird and Fred Cohen) straddled the 

two areas: Baird’s talk described recent progress on the 

cohomology of certain moduli spaces (chiefly achieved 

using homotopy theoretic techniques), while Cohen’s talk 

described the topology of “moment-angle complexes,” a 

class of objects that appears naturally in many geometric 

problems. 

About twenty people attended the conference. Roughly half 

the speakers were PhD students, postdoctoral fellows, or 

junior faculty. 

The previous Ontario Topology Seminar was held at 

McMaster University in 2002. A number of homotopy theorists 

went to Toronto to attend a concert of German songs 

by Lorna MacDonald (a professor in the Department of 

Music at the University of Toronto). Many years ago, when 

Lorna was at Westminster Choir College in Princeton, NJ, 

she got to know many topologists, including Tony Bahri, 

one of the conference organizers, who teaches in nearby 

Lawrenceville. Lorna’s concert provided a natural incentive 

to revive the Ontario Topology Seminar–the original working 

title for the conference, with apologies to Schubert, was 

“An die Homotopie.” Many of the conference participants 

(including all the organizers) attended the concert, which 

provided a grand finale to the conference. 

The Ontario Topology Seminar has been held periodically 

for more than thirty years at a number of institutions in 

Ontario, as well as Rochester, Detroit, and Montreal. This is 

the fifth time it has been hosted by the Fields Institute–the 

others were in 1995, 1996, 1997 and 1999. The organizers 

are grateful that the Fields Institute was willing to host the 

2007 Ontario Topology Seminar. 


Tom Baird (Toronto) 

Moduli spaces of flat connections over nonorientable surfaces 

Georg Biedermann (Western) 

Homotopy n-nilpotent groups 

Fred Cohen (Rochester) 

Interactions between moment-angle complexes and classifying 

spaces 

Don Davis (Lehigh) 

From invariant theory to homotopy groups 

Nan-Kuo Ho (National Cheng-Kung University) 

Yang-Mills connections over a nonorientable surface 

Lisa Jeffrey (Toronto) 

Connectedness of fibres of moment maps on based loop groups

David Klein (Toronto) 

Goldman flows on the moduli space of flat SU(2)-connections 

over a nonorientable surface 

Derek Krepski (Toronto) 

Obstruction to pre-quantization 

Jonathan Scott (Ottawa) 

The category of Lie-infinity algebras via co-rings over operads 

Paul Selick (Toronto) 

Anick’s fibration: fifteen years later 

Lisa Jeffrey 

Summer School in Iwasawa Theory 

August 9–13, 2007 

Held at McMaster University 

Organizers: Romyar Sharifi (McMaster), Manfred Kolster 

(McMaster), William McCallum (Arizona) 

The majority of the seventy-five participants were PhD students 

who had come from around the world to learn about 

this central and rapidly developing area in algebraic number 

theory. Four of the world’s leading experts gave lecture 

series designed to introduce students to the basics of the 

theory as well as to some of its most current developments. 

Iwasawa theory originated during the period from 1950 

to the 1970s in papers of Kenkichi Iwasawa, who studied 

the growth of class groups in towers of cyclic extensions 

of number fields. These class groups measure how far the 

ring of integers of such a finite extension of the rationals 

is from being a principal ideal domain. Iwasawa was 

especially interested in the structure of the p-parts of these 

class groups as modules over the Galois groups of the finite 

extensions in the tower in the case in which the order of 

these groups is a power of a prime p. Ralph Greenberg 

delivered a series of lectures introducing the audience to 

these foundational aspects of the subject. 

Today, Iwasawa theory concerns itself as well with the 

growth of interesting objects arising from arithmetic 

geometry, such as Selmer groups of elliptic curves. The 

“main conjecture” posits a relationship between the growth 

of such objects in towers and analytic objects called p-adic 

L-functions, in analogy to a statement for class groups of 

cyclotomic fields proven by Barry Mazur and Andrew Wiles 

in the 1980s. Robert Pollack gave a lecture series on the 

Iwasawa theory of elliptic curves. 


Much of the current interest in Iwasawa theory today is 

in understanding the growth of class groups and Selmer 

groups in non-abelian towers of number fields. Known as 

non-commutative Iwasawa theory, this fascinating and 

intricate subject has its own main conjectures, in which 

the p-adic L-functions are still in general only conjectural. 

John Coates gave a lecture series on the foundations of this 

subject. 

One of the most promising and important recent developments 

in Iwasawa theory is the extension of the techniques 

of Mazur and Wiles to study the structure of Selmer groups 

of elliptic curves, using four-dimensional Galois representations. 

Eric Urban gave a lecture series that first outlined 

the proof of the classical main conjecture and then of his 

recent work with Christopher Skinner on elliptic curves. 

In the opinion of the organizers, however, the highlight of 

the summer school was not the speakers but the students. 

They had come from all over the world–Canada, the United 

States, Europe, and from as far away as India and Japan–to 

learn about Iwasawa theory. In many cases, their advisors 

and departments generously supplemented funding from 

the Fields Institute and the National Science Foundation to 

make it possible for them to come. This summer school was 

to be about the students, to introduce them to the subject 

and give them a foundation in that should serve them well 

in their future mathematical careers. 

For each of the lecture series, students worked in groups 

with the speaker on a related project. They worked on their 

projects during four intense late-night sessions, to which 

the speakers generously donated their time and energy. By 

the third session, all the students were staying to work on 

their projects long after the sessions ended at 10 p.m. On the 

Summer School in iwasawa Theory workshop participants 

59


final morning of the conference, a number of students had 

their chance to deliver short lectures to the audience on a 

part of the project the group had completed. The students’ 

results were not only impressive, but informative, nicely 

complementing the speakers’ lecture series. 


John Coates (Cambridge) 

An introduction to non-commutative Iwasawa theory 

Ralph Greenberg (Washington) 

Introduction to Iwasawa theory 

Robert Pollack (Boston) 

Iwasawa theory of elliptic curves 

Eric Urban (Columbia) 

Eisenstein ideals and main conjectures in Iwasawa theory 

Romyar Sharifi 

Summer School on Computational Continuous 

Optimization 

August 11–12, 2007 

International Conference on Continuous Optimization 

(ICCOPT) 

Modeling and Optimization: Theory and Applications 

(MOPTA) 

August 13–16, 2007 

Both held at McMaster University 

60 

iCCopT Conference participants 

Organizers: Tamás Terlaky (McMaster), Richard Caron 

(Windsor), Thomas Coleman (Waterloo), Antoine Deza 

(McMaster), Tom Marlin (McMaster), Jiming Peng 

(UIUC), Barosz Protas (McMaster), Anthony Vannelli 

(Guelph), Henry Wolkowicz (Waterloo) 

The ICCOPT-MOPTA conference attracted some 450 

researchers from 35 countries. It featured two plenary sessions 

in which Adrian Lewis (Cornell) spoke on Nonsmooth 

Optimization: Fundamentals and Applications and Larry 

Biegler (Carnegie Mellon) on Optimization Methods for 

Chemical Process Engineering; 12 semiplenary presentations 

by leading experts of the represented areas ranging from 

fundamental theoretical topics, through algorithmic and 

computational methods, to emerging application areas. The 

conference had nine parallel sessions that were organized 

in thematic streams covering all subject areas of continuous 

optimization and many of the important engineering 

application areas, such as design optimization and chemical 

control. 

The conference also featured the presentations of the finalists 

of the Young Researcher Prize. Twenty-one of the best 

papers written since the last ICCOPT competition in 2004, 

submitted by Ph.D. students and recent graduates worldwide, 

were evaluated by a jury of members from Japan, 

Austria, Canada, USA and the Netherlands. Selection of 

the finalists and the winner was based on the quality of 

the paper, including originality of the results and potential 

impact. The three finalists were: Alexandre Belloni (Duke, 

First prize), Mung Chiang (Princeton) and Eissa Nematollahi 

(McMaster).

Another conference highlight was the participation of Fred 

Eisenberger, the Mayor of Hamilton, who welcomed the 

participants at the conference banquet at LIUNA Station 

where a dance group demonstrated some of the spectacular 

aspects of Canada’s aboriginal culture. 

The ICCOPT-MOPTA conference was preceded by a 

Summer School for PhD students and young researchers. 

About 50 participants enjoyed excellent lectures for 

two days. The theme of the first day was Experimental 

Mathematics with Variational Applications, with lectures by 

Jon Borwein, David Bailey and Russell Luke. The goal of 

this course was to present a coherent variety of accessible 

examples of modern variational mathematics where intelligent 

computing plays a significant role and, in doing so, 

to highlight some of the key algorithms and teach some of 

the key experimental approaches. The theme of the second 

day was Grid-computing for optimization: modeling and 

solution, with lectures by Michael Ferris, Jeff Linderoth and 

Stephen Wright. This course introduced the participants 

to computational grids, where computing platforms are 

created by harnessing unused CPU cycles from a variety of 

distributedly-owned workstations and clusters. Condor is a 

free and popular software tool from which such federated 

computing platforms can be built. Grids can be very powerful, 

but they are difficult to use effectively. 

ICCOPT is a tri-annual conference of the Mathematical 

Programming Society; MOPTA is an annual workshop in 

Southern Ontario, which was organized by the Advanced 

Optimization Lab (AdvOL) at McMaster for the first five 

years, and by University of Windsor in 2005 and University 

of Waterloo in 2006. The next MOPTA conference will be 

held at the University of Guelph in 2008. 

Sponsors: 

The Fields Institute 

MITACS 

McMaster University 

University of Waterloo 

University of Windsor. 


Larry Biegler(Carnegie Mellon University) 

Optimization Methods for Chemical Process Engineering 

Adrian Lewis (Cornell) 

Nonsmooth Optimization: Fundamentals and Applications 

Mihai Anitescu (Argonne National Laboratory) 

Emerging design challenges in the advanced nuclear fuel cycle 


Phil Gill (San Diego) 

Numerical Linear Algebra and Optimization 

Jacek Gondzio (Edinburgh) 

Large Scale Optimization with Interior Point Methods 

Nick Gould (Oxford University and Rutherford Appleton 

Lab) 

Nonlinear Programming Methods 

Hubertus Th. Jongen (RWTH Aachen University) 

Nonlinear Semi-Infinite Programming: Structural Analysis 

Pablo Parrilo (MIT) 

Optimization with Polynomials 

Andrew Philpott (Auckland) 

Stochastic optimization in electricity pool markets 

Nick Sahinidis (Illinois) 

Optimization in Biology 

Katya Scheinberg (IBM, Yorktown) 

Model Based Derivative Free Optimization 

Melvyn Sim (National University of Singapore, Singapore- 

MIT Alliance) 

New robust optimization models for addressing stochastic 

optimization problems 

Hiroshi Yamashita (Mathematical Systems, Inc., Tokyo) 

Primal-dual methods for NLP and NLSDP 

Yinyu Ye (Stanford) 

Further Developments of SDP for Sensor Network 

Localization 

Tamás Terlaky 

6 th International Conference on Unconventional 

Computation 

August 13–17, 2007 

Hosted by Queen's 

Organizers: Selim Akl, Kamrul Islam, Marius Nagy, Yurai 

Núñez, Kai Salomaa, and Henry Xiao (Queen’s) 

Queen’s School of Computing hosted the Sixth International 

Conference on Unconventional Computation, UC’07, 

held to discuss ideas of computation that surpass the traditional 

Turing model. 

Participants began to arrive Sunday night from universities 

and industries that spanned six continents. After a pleasant 

social gathering Sunday night, the conference began bright 

and early Monday morning with a talk from Michael Arbib 

61


on the continuing unconventionality of neural computing. 

Arbib’s notion of persistent and dynamic unconventionality 

set the tone for the conference. Ideas from diverse 

disciplines were presented as inspiration for various computational 

algorithms. For example, Monday afternoon saw 

many new and novel concepts, as open problems in the field 

of unconventional computations were presented. Monday 

closed with a walking tour of historic Kingston and Queen’s 


Tuesday oriented itself towards quantum physics and the 

way in which it lends itself to computation. Gilles Brassard 

gave a tutorial on quantum information processing in the 

afternoon, following a morning of heated debates on how 

information is best categorized and utilized. In the evening, 

conference participants toured local art at Delvalle’s Art 

Corner. 

Wednesday’s subject matter grew out of nature’s evolving 

wisdom. Roel Vertegaal gave a presentation on creating 

user-interfaces that are harmonious with their environment. 

This was followed by a workshop on biologically 

inspired computations. To close the day, conference participants 

enjoyed Fort Henry’s breathtaking sunset ceremony. 

Lila Kari began Thursday by lecturing on self-assembly in 

nanocomputation systems. Problems and challenges in ad 

hoc and sensor networks were presented in the afternoon by 

Hossam Hassanein. The day closed with a friendly banquet 

accompanied by a jazz quartet, where animated discussion 

was a hallmark of the night. 

Tal Mor furthered consideration of quantum computing 

when he presented his work on algorithmic cooling. UC’07 

closed Friday on a lively note when the floor was opened 

for discussion on the week’s presentations. In tune with the 

week, ideas were exchanged on the exact nature and power 

of computations–despite the varied inputs, no universally 

accepted answer was computed. 

This conference was sponsored by the Fields Institute, 

MITACS, IEEE Kingston Section, and Queen’s University. 

Keynote Lectures: (in alphabetical order) 

Michael Arbib (USC) 

How neural computing can still be unconventional after all 

these years 

Lila Kari (Western) 

Nanocomputing by self-assembly 

Tal Mor (Technion, Israel Institute of Technology) 

Algorithmic cooling: putting a new spin on the identification 

of molecules 

62 

Roel Vertegaal (Queen’s) 

Organic user interfaces (oui!): designing computers in any 

way shape or form 

Tutorials: 

Gilles Brassard (Montréal) 

Quantum infomation processing 

Hossam Hassanein (Queen’s) 

Wireless ad hoc and sensor networks–challenges and opportunities 

Krista Kostroman 

Workshop on Cellular Automata 

August 27–29, 2007 

Organizers: Henryk Fuks´ (Brock) and Anna Lawniczak 

(Guelph) 

Scientific Program Committee: Andrew Adamatzky (West 

of England), Henryk Fuks´ (Brock), Anna Lawniczak 

(Guelph), Danuta Makowiec (Gdansk), Thomas Worsch 

(Karlsruhe) 

Over seventy researchers from sixteen different countries 

attended Automata 2007, presenting and discussing the 

newest developments in the theory and applications of cellular 

automata and discrete complex systems. With forty 

talks and a poster session, the program of the workshop was 

very intense. It covered the beauty of the research in cellular 

automata (CA) from the perspective of mathematics, 

computer science and statistical physics, with applications 

in diverse areas, such as epidemiology, sensor networks, 

road traffic, tumour growth, and cardiac pacemakers. The 

multidisciplinary synergy, enhanced by that between theoreticians 

and applied researchers, contributed to the success 

of Automata 2007, the best attended meeting in the history 

of Automata workshops since 1995. 

Among the highlights of the scientific program was the talk 

by Marcus Pivato (Trent) on the emergent defect dynamics 

in two-dimensional CA. In the past, many researchers 

studied dynamics of interacting coherent structures in 

one-dimensional CA, but the large-scale search conducted 

by Pivato and his collaborators uncovered many exciting 

examples of two-dimensional CA exhibiting emergent 

defect dynamics with striking visual appearance and rich 

mathematical structure. 

The session devoted to lattice gas cellular automata (LGCA) 

was another highlight of the conference. It demonstrated 

how much progress has been achieved since one of the first

LGCA conferences was organized by Raymond Kapral and 

Anna Lawniczak and held at the Fields Institute in1993. 

Several participants who attended the 1993 conference 

returned back to the Fields to present their research results 

this year. One of them, Raul Retchman, demonstrated with 

Franco Bagnoli (Florence) how a simple lattice gas cellular 

automaton can be used to construct a direct link between 

dynamical indicators such as the Lyapunov exponent and 

statistical physics indicators such as the Boltzmann H 

function. Their elegant and simple model exploits the idea 

of the Boolean derivative, and most importantly, takes full 

advantage of the discrete nature of the underlying space. 

Automata 2007 provided an excellent forum for scientific 

exchanges and research interactions among researchers 

from various countries and from various theoretical and 

applied disciplines. Many times it bridged the divide among 

researchers working on the same kind of problems under 

different discipline names. One such example is the study 

of properties of asynchronous cellular automata–that is, 

cellular automata that are updated sequentially or semisequentially. 

One may study these properties by considering 

all possible updating orders, which is possible only on 

relatively small lattices. This is the most common technique 

used in the study of Sequential Dynamical Systems (SDS). 

Another possibility is to consider large lattices, and sample 

update orders stochastically instead of considering all of 

them. One of the SDS experts, Henning Mortveit (Virginia 

Tech), found that another Automata participant, Nazim 

Fates, is using the stochastic sampling technique to study 

asynchronous CA, while looking at very similar problems. 

workshop on Cellular automata participants 


Automata 2007 created synergy between theory and 

applications and demonstrated the relevance of the field in 

resolving pressing problems in society and technology. Jian 

Yuan presented an application of CA in the topological control 

of wireless sensor networks in order to achieve desired 

emergent network properties. The theoretical results of 

this study are important for resolving technical issues in 

some sensor networks being used during the forthcoming 

2008 Olympics in Beijing. Andreas Deutsch (Dresden), 

another participant of the 1993 conference, discussed the 

importance of CA and LGCA methodologies for studying 

pattern formation in biological systems and illustrated this 

by considering Myxobacteria and brain tumor growth. 

Vittoria Colizza (Turin) presented a large-scale stochastic 

computational model to study the spread of epidemics and 

discussed applying this model to study the spread of SARS 

in Canada. 

All participants enjoyed the facilities of the Fields Institute, 

in particular the lobby that provided a cozy yet spacious 

focal point for attendees to meet and interact. The banquet 

at the University of Toronto Faculty Club was well attended. 

The participants and their accompanying guests enjoyed 

it and admired the paintings of the Group of Seven during 

the reception. The youngest guest of the evening was 

the one year old son of J.C.S. Tuoh Mora of Universidad 

Autonoma Del Estado De Hidalgo, Mexico. All the attendees 

of Automata 2007 were fascinated and impressed by the 

multiethnic and multicultural diversity and atmosphere of 

Toronto. Many of them could not resist exploring the many 

cuisines of the city. 

63



Ramon Alonso-Sanz (Polytechnic University of Madrid) 

Cellular automata with memory 

Franco Bagnoli (Florence) 

Boolean derivatives: chaos and synchronization in cellular 

automata 

Silvio Capobianco (Reykjavik) 

Surjectivity and surjunctivity of cellular automata in Besicovitch 

topology 

Vittoria Colizza (Institute for Scientific Interchange, Turin) 

Are global epidemics predictable? The SARS case study 

Vahid Dabbaghian-Abdoly (Simon Fraser) 

A cellular automata model of the spread of HIV in a community 

of injection drug users 

Andreas Deutsch (Technical University Dresden) 

Cellular automaton modelling of spatio-temporal pattern 

formation in interacting cell systems 

Witold Dzwinel (Agh University of Science and Technology) 

Can the spatially extended populations replicate the logistic 

map? 

Samira El Yacoubi (Perpignan) 

A cellular automata approach for discrete-time distributed 

parameter systems 

Nazim Fatès (Nancy 1) 

Prolegomena to a theory of asynchronous and probabilistic 

cellular automata 

Paola Flocchini (Ottawa) 

Cellular automata and dynamic monopolies 

Eric Goles (Universidad Adolfo Ibañez) 

Parallel and serial dynamics in Boolean networks 

Janusz A. Hołyst (Warsaw University of Technology) 

Self-organized criticality and co-evolution of network structure 

and dynamics 

Katsunobu Imai (Hiroshima) 

On the influence of symmetries and neighborhoods on 

constructing two dimensional number-conserving cellular 

automata rules 

Brunon Kaminski (Nicolaus Copernicus) 

Space-time directional Lyapunov exponents for cellular 

automata 

64 

Raymond Kapral (Toronto) 

Simple dynamics for complex systems 

Maria Elena Lárraga (UAEM) 

Traffic flow based on safety embedded notions 

Pietro Lio (Cambridge) 

Simulating the spread of infectious disease using a spatial, 

agent based model 

Danuta Makowiec (Gdansk) 

On cellular automata modeling of cardiac pacemaker 

Matthew Macauley (Santa Barbara) 

Order independence in asynchronous cellular automata 

Angelo B. Mingarelli (Carleton) 

A classification scheme of fuzzy cellular automata with applications 

to ECA 

Juan Carlos Seck Tuoh Mora (Universidad Autónoma del 

Estado de Hidalgo) 

Computational implementation of De Bruijn networks and 

the calculus of pre-images in several steps for one-dimensional 

cellular automata. 

Kenichi Morita (Hiroshima) 

On universal 1-d reversible cellular automata 

Henning S. Mortveit (Virginia Tech) 

Phase space equivalences of sequential dynamical systems 

Katsuhiko Nakamura (Tokyo Denki University) 

Towards a basis for parallel language recognition by cellular 

automata 

Hidenosuke Nishio (Kyoto) 

Fix a local function and change neighborhoods 

Pedro P.B. de Oliveira (University Presbiteriana Mackenzie) 

Evolutionary computation techniques to look for cellular 

automata rules 

Marcus Pivato (Trent) 

Emergent defect dynamics in two-dimensional cellular 

automata 

Edward Powley (University of York) 

Classifying cellular automata by automorphisms of transition 

diagrams 

David Pritchard (Waterloo) 

Efficient divide-and-conquer simulations of symmetric FSAs

Raul Rechtman (UNAM) 

Entropy and chaos in a discrete hydrodynamical system 

Klaus Sutner (Carnegie Mellon) 

Classification and complexity 

Burton Voorhees (Athabasca) 

Transformations of binary valued additive rules 

Gabriel Wainer (Carleton) 

The Cell-DEVS formalism: modelling and simulating 

discrete-event cell spaces 

Thomas Worsch (Karlsruhe) 

How to achieve universality in a CA using the same local rule 

but different neighborhoods 

Reem Yassawi (Trent) 

Emulating substitution shifts using cellular automata 

Jian Yuan (Tsinghuan) 

Applying cellular automata in topology control of wireless sensor 

networks 

Jean-Baptiste Yunès (Paris, Diderot) 

New extensions to some firing squad synchronization solutions 

Anna Lawniczak 

SPARC Workshop on Data Assimilation 


Organizers: Saroja Polavarapu and Theodore Shepherd 

(Toronto) 

Any mathematician walking into the Fields Institute during 

the week of September 4–7 would have been surprised 

to see the ground floor filled with posters on atmospheric 

science, many showing colourful images of atmospheric 

observations. The occasion was the annual workshop of 

the SPARC (Stratospheric Processes And their Role in Climate) 

project of the World Climate Research Programme 

(WCRP), which attracted over fifty atmospheric scientists 

from around the world. 

Atmospheric data assimilation is an application of control 

theory, whereby atmospheric observations are combined 

with model predictions to produce an optimal estimation 

of the state of the atmosphere at a particular time, called 

an analysis. It was originally developed to produce initial 

conditions for weather forecasts, but the sequence of such 

states provides a four-dimensional picture of the atmosphere’s 

time evolution and can be studied in its own right 


to better understand atmospheric processes. For studies of 

the troposphere, such long-term analyses are now a staple of 

climate science. 

The SPARC project (www.atmosp.physics.utoronto.ca/ 

SPARC/) aims to stimulate and coordinate international 

research related to the role of the stratosphere (the region 

of the atmosphere between about 10 and 50 km altitude, 

containing the ozone layer) in climate. SPARC is interested 

in data assimilation partly because of the value of stratospheric 

analyses for furthering SPARC science, and partly 

because of what the process of data assimilation can tell us 

about the workings of the stratosphere. 

This might seem a long way from mathematics. However 

atmospheric data assimilation is built on mathematical 

principles (from control theory) and many data assimilators 

come from a mathematical background. Yet the assumptions 

of the theory are never really satisfied in practice and 

it is essential to combine the mathematics of data assimilation 

with a good understanding of the physical principles 

governing atmospheric behaviour, in order to achieve 

scientific progress. The purpose of the SPARC Data Assimilation 

Working Group is to further this development in the 

context of the stratosphere, through annual workshops. 

This year’s workshop was combined with a workshop on 

International Polar Year, because of the strong synergy 

between SPARC activities in the two areas. The program 

consisted of both invited and contributed talks, poster 

presentations, and open discussions. As in past workshops, 

the participants were about evenly divided between data 

The mesopheric polar vortices in GeoS, waCoM, SaBeR, 

and eoS-MlS 

V. Lynn Harvey (Colorado) 

65


assimilators and “process” scientists, and there was even a 

card-carrying mathematician from Toulouse! The relaxed 

schedule allowed for extensive interactions and discussions, 

to which the venue also effectively contributed. 

A full report on the science can be found in the January 

2008 issue (No. 30) of the SPARC Newsletter (www. 

atmosp.physics.utoronto.ca/SPARC/Newsletters.html). 

Environment Canada helped significantly with workshop 

costs, while the WCRP and the SPARC International 

Project Office (hosted by the Physics Department at the 

University of Toronto) provided travel support to some of 

the participants. 

This may have been the first atmospheric science workshop, 

but it won’t be the last. The event was so successful that a 

SPARC workshop was planned for March 2008 in Toronto. 

The Joint SPARC Gravity Wave and DynVar Planning 

Workshop took place March 26–28 in Toronto. 


Didier Auroux (Toulouse) 

Back and forth nudging algorithm for data assimilation 

problems 

Frank Baier (German Aerospace Center) 

The impact of ground based ozone monitoring on stratospheric 

ozone assessments: A case study using sequential and 

variational data assimilation 

Mark P. Baldwin (Northwest Research Associates) 

How will a changing stratosphere affect high-latitude climate? 

Craig Benson (UMBC) 

Detection of Antarctic ice polar stratospheric clouds from 

AIRS assimilation 

Pablo Canziani (in absentia – presented by E. Farahani) 


Stratosphere-troposphere coupling studies at high southern 

latitudes and Antarctic historic data analysis 

Richard L. Collins (Alaska Fairbanks) 

Pan-Arctic study of the coupled tropospheric stratospheric and 

mesospheric circulation 

Ronald M. Errico (UMBC) 

General characteristics of stratospheric singular vectors 

Jean de Grandpré (Environment Canada) 

On the extraction of wind information from the 4D-var 

assimilation of chemical constituents 

66 

V. Lynn Harvey (Colorado) 

The mesospheric polar vortices in GEOS, WACCM, SABER, 

and EOS-MLS 

Michaela I. Hegglin (Toronto) 

The benefits of in-line advection – Assessing the transport 

characteristics of the CMAM-DAS 

Karl Hoppel (Naval Research Laboratory) 

Stratospheric and mesospheric assimilation using the 

NOGAPS-ALPHA/NAVDAS forecast model 

Mike Keil (Met Office) 

Impact of different representations of ozone on tropospheric 

weather forecasts 

Heiner Körnich (Stockholm) 

Equatorial waves as a balance relationship in global data 

assimilation 

Ruth S. Lieberman (Northwest Research Associates, Inc.) 

Intercomparison and fusion of EOS/MLS and TIMED/ 

SABER temperatures 

Gloria Manney (Jet Propulsion Laboratory & NM Tech 

University) 

Near-real-time processing plans for aura MLS data for use in 

data assimilation 

Stratopause and tropopause evolution and transport and 

implications for assimilated analyses 

Charles McLandress (Toronto) 

An overview of the dynamics of the mesosphere and lower 

thermosphere 

Richard Menard (Environment Canada) 

Coupled chemistry-dynamics data assimilation 

Lisa Neef (KNMI) 

Gravity waves in four-dimensional data assimilation 

Yulia Nezlin (Toronto) 

A study of the CMAM_DAS using simulated observations 

Shuzhan Ren (Toronto) 

The constraint of data assimilation in the stratosphere and 

troposphere on mesospheric motions 

Matt Reszka (Environment Canada) 

New 3D-Var dynamical constraints at Environment Canada 

Yves Rochon (Environment Canada) 

3D-FGAT assimilation of MIPAS-IMK and GOMOS chemical 

data

Adam Scaife (Met Office) 

Stratospheric influences on surface winter climate and prospects 

for seasonal forecasting 

Jörg Schwinger (Cologne) 

Cross validation of MIPAS/SAGE II and MIPAS/HALOE 

trace gas observations by means of four-dimensional variational 

assimilation 

Kimberly Strong (Toronto) 

Investigating middle atmospheric chemistry at the Polar Environment 

Atmospheric Research Laboratory (PEARL) 

Kris Wargan (GSFC and SAIC) 

Variability of assimilated ozone in the upper troposphere and 

lower stratosphere 

Valery A. Yudin (NCAR) 

Constraining zonal mean flow and diurnal tide by spaceborne 

data 

Theodore Shepherd 

Workshop on Geometrization of Probability 



Organizers: Vitali Milman (Tel-Aviv) and Vladimir Pestov 

(Ottawa) 

The workshop was devoted primarily to a new development 

in asymptotic geometric analysis. It has become 

clear in recent years that the picture offered by asymptotic 

convexity theory (where the word “asymptotic” means that 

dimension of bodies involved increases to infinity), as well 

as by asymptotic theory of normed spaces, is incomplete 

and that future development requires its extension to a 

much more general category of log-concave measures. 

Because the measures considered are positive and finite, 

only normalization distinguishes them from probability 

measures, and for this reason we call this development 

“Geometrization of Probability.” In this extension the role 

of a convex body, K, is played by the uniform (i.e. volume) 

distribution on K. In the language of functions (distribution 

densities) this corresponds to the characteristic 

(indicator) function of the set K. 

Such extensions first led to a number of very interesting 

functional versions of classical geometric inequalities (such 

as, for example, the Santalo and Uryhson inequalities) and 

required novel notions–for instance a version of polarity for 

functions. 


Two lectures by Shiri Artstein-Avidan were devoted to a 

consequence of this development. In order to extend the 

notion of polarity from the purely geometric category to 

the functional form, one needs first to understand what 

is meant by polarity. To this end, Shiri discussed novel 

characterizations of two classical transforms in analysis: 

The Fourier transform and the Legendre transform. As a 

particularly attractive characterization, it was proved that 

the only involution on the space of convex functions that 

reverses order is the Legendre transform with respect to 

various Euclidean structures. 

However, the most interesting outcome of this extension 

is, first, that some typical probabilistic results (and the way 

of thinking) are interpreted and proved in the geometric 

framework, and, secondly and, perhaps, most importantly, 

the extension of the geometric approach to the log-concave 

category is needed to solve some central problems of a 

purely geometric nature. 

The most spectacular result in this direction was, undoubtedly, 

presented by Boaz Klartag who in two lectures 

gave participants the flavor of his recent solution of the 

so-called Central Limit Problem for convex bodies (now 

one may also add the Central Limit Theorem for logconcave 

measures). Roughly stated, the result is this: any 

high-dimensional convex body has marginals that are well 

approximated by the gaussian distribution. 

Robert McCann delivered two lectures on an elegant geometric 

construction related to the regularity theory of the 

optimal transportation problem in smooth manifolds. The 

participants learned that, roughly speaking, the optimal 

transportation map is continuous and smooth when a certain 

natural pseudo-Riemannian metric has, in some sense, 

a non-negative sectional curvature. 

In addition to these three mini-courses, the workshop 

program included a number of invited talks of varying 

duration. One-hour lectures by Alexander Litvak, Nicole 

Tomczak-Jaegermann, and Elisabeth Werner were a tasteful 

blend of geometry and probability. Tomczak-Jaegermann 

described a certain property of random subgaussian matrices 

and its applications to geometric problems regarding 

sections of convex bodies and random polytopes. Alexander 

Litvak and Elisabeth Werner considered order statistics of 

some sequences of random variables. A wealth of results 

was presented, including applications to the practical 

approximate reconstruction problem. Open problems with 

an appealing formulation regarding gaussian random vectors 

were also proposed. 

67


Staszek Szarek discussed some non-commutative connections 

of asymptotic geometric analysis, giving us a taste of 

geometry in a non-commutative setting. 

Emanuel Milman and Sasha Sodin described the effects 

that certain convexity assumptions have on the uniform 

probability measure on the relevant domain (or manifold). 

In Sodin’s talk, it was proved that the value measure on a 

uniformly convex body satisfies a certain (explicit) isoperimetric 

inequality. In Milman’s talk, connections were 

discussed between the isoperimetric problem, concentration 

and the spectral gap of the corresponding Laplace 

operators; in particular, that under convexity assumptions 

well known implications can be reversed. 

Dmitry Ryabogin told us about a surprising distinction 

between zonoids of odd and even dimension. Suppose a 

convex set has the property that its boundary is “locally the 

boundary of a zonoid” in a certain natural sense. Does it 

imply that the set is necessarily a zonoid? The answer is that 

it depends on the dimension: in even dimensions, the set 

is necessarily a zonoid, but in odd dimension the answer is 

negative. In other words, there is a local characterization of 

zonoids, in some sense, only in even dimensions. 

The workshop attracted eighteen participants, who were 

able to hold a large number of informal discussions among 

themselves. Overall, it was a successful event of high 

intensity, and the only thing one may regret is that too few 

participants came from the two Ottawa-based universities. 

Mini-courses: (in alphabetical order) 

Shiri Artstein-Avidan (Tel-Aviv) 

Characterization of duality 

Boaz Klartag (Princeton and the Clay Institute) 

A central limit theorem for convex bodies 

Robert McCann (Toronto) 

Continuity, curvature, uniqueness, and general covariance of 

optimal transportation 

Lectures: (as listed on program itinerary) 

Alexander Litvak (Alberta) 

On expecations of order statistics 

Emanuel Milman (IAS) 

Weak-type Poincaré inequalities and concentration of Lipschitz 

functions on convex domains 

Dmitry Ryabogin (Kansas State) 

On the local equatorial characterization of zonoids 

68 

Sasha Sodin (Tel-Aviv) 

An isoperimetric inequality for uniformly convex bodies 

Stanislaw Szarek (Case Western Reserve and Paris 6) 

Convex sets of quantum information theory 

Nicole Tomczak-Jaegermann (Alberta) 

Estimates for linear images of random subgaussian vectors 

Elizabeth Werner (Case Western Reserve) 

Maxima and minima of sequences of random variables 

Vladimir Pestov 

Canadian Computer Algebra and Dynamic Geometry 

Systems in Mathematics Education Conference 


Held at Nipissing University 

Organized by members of the Nipissing University Mathematics 

Education, Research, and Information Council 

(NUMERIC) 

Computer algebra systems (CAS) and interactive geometry 

software applications are becoming more prevalent in 

school and university mathematics curricula. The CCA- 

DGME conference sought to address this reality through 

a unique combination of conversation and experience. 

The conference structure and registration were organized 

around two different tracks: one which involved Working 

Groups that examined issues of teacher practice and related 

research at the elementary, secondary, and post-secondary 

levels; and, a second involving a series of Technology Workshops 

which focused more on the exploration of a variety of 

CAS-based and interactive geometry software applications. 

Participants within both tracks shared common keynote 

speaker sessions, meals/refreshment breaks, as well as 

several technology and open discussion sessions during the 

weekend. 

Keynote addresses were delivered by Zsolt Lavicza (Cambridge), 

Chantal Buteau (Brock), Walter Whiteley (York), 

Carolyn Kieran (UQAM), Nick Jackiw (KCP Technologies), 

Kate Mackrell (Queen’s) presenting with Patrick St-Cyr 

(Cabrilog), and Nathalie Sinclair (Simon Fraser). Among 

the issues discussed during these talks were the following:

CCaDGMe conference participants 

• university professor beliefs/conceptions relating to teaching 

with technology 

• factors affecting system/departmental shifts in technology 

use within an undergraduate program 

• the importance of 2- and 3-D modelling, i.e., combining 

visual and kinaesthetic approaches in --teaching considerations 

in designing rich CAS-based tasks for secondary 

students 

• the use of dynamic geometry software in modelling discrete 

and continuous mathematics 

• the effectiveness of having young learners (K-8) model 

mathematical concepts and explore new ideas with technology 

Technology/software companies represented at the 

CCADGME conference included Autograph, Cabrilog, 

Cinderella, GeoGebra, KCP Technologies, Maplesoft, Texas 

Instruments, and Wolfram. The conference website features 

a variety of resources made available by participants, as well 

as links to related technology sites dealing with Computer 

Algebra Systems (CAS) and interactive geometry software. 

Furthermore, at the time of this writing, streamed digital 

video recordings of the seven keynote addresses are also 

being prepared for public access via the conference website. 

See www.nipissingu.ca/ccadgme/index.htm 

Technology in mathematics education may indeed possess 

rich potential for mathematical teaching and learning at 

all levels. However, this optimism must be continually 

tempered with legitimate concerns raised by colleagues 

from both mathematics and mathematics education. The 

CCADGME conference facilitated rich discussions surrounding 

these controversial yet significant issues which 

will no doubt continue to characterize, at least in part, the 

21 st century educational project. 


Sponsors: 

Social Sciences and Humanities Research Council of 

Canada (SSHRC) 

Nipissing University 

Fields Institute of Research in Mathematical Sciences 

Several technology/software vendors. 


Chantal Buteau (Brock) 

Going from CAS to MICA: Integration of technology in the 

Brock curriculum 

Nick Jackiw (KCP Technologies) 

Design, discourse, and discrete mathematics 

Carolyn Kieran (UQAM) 

CAS in secondary school algebra: Designing tasks 

Zsolt Lavicza (Cambridge) 

Technology related research issues at the university level 

Kate Mackrell (Queen’s), Patrick St-Cyr (Cabrilog) 

Cabri usage in elementary school 

Nathalie Sinclair (Simon Fraser) 

Modelling practices with the geometer’s sketchpad 

Walter Whiteley (York) 

Math with eye and hand: GSP, manipulatives, and postsecondary 

math 

Daniel Jarvis 

Workshop on Algebraic Varieties of Higher Dimensions 

with Special Emphasis on Calabi-yau Varieties and 

Mirror Symmetry 

November 3–4, 2007 

Organizers: James D. Lewis (Alberta), Noriko Yui (Queen’s) 

There were 11 one-hour talks in this the bi-annual workshop, 

covering topics in the rapidly developing areas in the interface 

of number theory, algebraic geometry and string theory. 


Vincent Bouchard (Harvard) 

Mirror symmetry, matrix models and enumerative geometry 

Chris Brav (Queen’s) 

Braid groups and the McKay correspondence 

Ethan Cotterill (Queen’s) 

Rational curves of degree 11 on a general quintic threefold 

69


Amanda Folsom (Wisconsin) 

Harmonic Maass forms and Borcherds products 

Alice Garbagnati (Milano) 

Symplectic automorphisms on K3 surfaces 

James Lewis (Alberta) 

Cycles on varieties over subfields of the complex numbers 

Ling Long (Iowa State) 

Modularity of algebraic varieties 

Michael Rose (UBC) 

Mirror symmetry and l-adic Chen-Ruan cohomology 

Yifan Yang (National Chiao Tung University/Queen’s) 

Monodromy and Sp4 modularity of Picard-Fuchs differential 

equations for Calabi-Yau threefolds 

Jeng-Daw Yu (Queen’s) 

Unit roots of Calabi-Yau varieties in the Dwork families 

Yuri Zarhin (Penn State) 

Cubic surfaces and cubic threefolds, Jacobians and intermediate 

Jacobians 

Noriko Yui 

Conference on the Occasion of the 60 th Birthday of 

Andreas Blass 

November 9–10, 2007 

Organizers: Claude Laflamme (Calgary), Juris Steprāns 

(Fields and York), Yi Zhang (Beijing) 

70 

andreas Blass 

The November 9-10 conference honouring Andreas Blass 

was an opportunity for his former students, post doctoral 

fellows and many collaborators to present their recent 

research, keeping in mind Andreas’ tastes and interests. 

Many of the speakers prefaced their talks with recollections 

of Andreas’ well known patience, generosity with his time 

and mathematical insights, and his willingness to respond 

to unknown correspondents from all over the globe. 

A recent query on MathSciNet revealed that Andreas Blass 

is the author of 172 reviewed articles on topics covering 

an astounding range of mathematics. He has important 

publications in the theory of algorithms, models of number 

theory, probability, zero-one laws, geometry, finite 

combinatorics, infinitary combinatorics, polynomial time 

computation, abelian groups, ring theory, operator theory, 

linear logic, category theory and, of course, almost all 

branches of set theory. One should expect the list of titles 

of a conference in honour of such a mathematician to be 

eclectic, and indeed, this one was. 

On the one hand, it could easily be guessed that there 

would be talks on set theoretic topics, talks such as Tomek 

Bartoszynski’s on the Borel conjecture or Alan Dow’s on 

mappings and images of the Cech-Stone remainder of the 

real line and of the integers. It could already be considered 

unusual to have these topics alongside a talk such as Bruce 

Sagan’s on a game theoretic version of the Erdos-Szekeres 

Theorem–a theorem asserting the existence of long monotone 

sub-sequences of finite permutations. But topping 

it off by having Andre Scedrov’s discussion of a formal 

analysis of the Kerberos 5 authentication protocol follow 

Todd Eisworth’s talk on the combinatorics of successors 

of singular cardinals is juxtaposition not likely to happen 

again in the near future. 

However, there was one area of research that figured in 

many of the talks: NCF, the Near Coherence of Filters. This 

is an assertion about filters on the natural numbers, an 

assertion which can be neither proved nor refuted without 

appealing to set theoretic axioms beyond the usual ones. 

One formulation says that for any two filters on the natural 

numbers there is a partition of the natural numbers into 

disjoint finite intervals such that if X belongs to one filter 

and Y to the other then there is at least one interval from 

the partition which meets both X and Y. The NCF hypothesis 

first appeared in joint work of Blass and Gary Weiss, one 

of the speakers at the conference. Weiss had been interested 

in the question of Brown, Pearcy and Salinas of whether 

the ideal of compact operators in the algebra of bounded 

operators on separable Hilbert space could be expressed as

the sum of two proper sub-ideals. Blass and Weiss were able 

to show that the Continuum Hypothesis implied an affirmative 

answer, but their proof showed that assuming the 

negation of NCF sufficed. Later, Blass was able to show that 

NCF was equivalent to a negative answer to the question of 

Brown, Pearcy and Salinas. 

It is interesting to note the confidence Blass had in the 

importance of this principle which he had isolated. Years 

before he and Shelah had shown the consistency of the 

axiom in 1989, he was already examining consequences of 

NCF. His confidence in the importance of NCF has proven 

to have been more than well-founded. Together with the 

applications to the theory of operators, there are also consequences 

to the study of abelian groups and continua theory. 

For example, the remainder of the Cech-Stone compactification 

of the half-line has one composant if and only if NCF 

holds. The axiom can also be used to calculate the number 

of slenderness classes of abelian groups. 

Several of the invited speakers (Mildenberger, Laflamme, 

Brendle, Eisworth, Gobel, Dow, Bartoszynski) are experts 

on NCF, its applications, or the related combinatorics of 

cardinal invariants of the continuum. The conference 

provided both students and experienced researchers the 

opportunity to learn about the latest developments in this 

area. 

The study of NCF is characteristic of Andreas Blass’ taste 

and interest in mathematics. The opening remarks of Yuri 

Gurevich of Microsoft Research sum these up very well. 

Yuri, with whom Andreas works on questions in computer 

science, recalls asking him why he is attracted to abstract 

problems from pure mathematics when he could easily 

devote himself to “important” problems, such those coming 

from Microsoft. After a moment’s reflection Andreas 

shrugged and replied, “They’re fun.” 


Tomek Bartoszynski (NSF) 

Around the Borel Conjecture 

Jörg Brendle (Kobe) 

Distinguishing groupwise density numbers 

Alan Dow (North Carolina) 

Maps and special points of remainders 

Todd Eisworth (Ohio) 

Club-guessing and Coloring Theorems 

Rüdiger Göebel (Duisburg-Essen) 

Decompositions of reflexive groups and Martin’s axiom 


Yuri Gurevich (Microsoft Research) 

Zero-one laws in discrete mathematics 

Neil Hindman (Howard) 

A New and Stronger Central Sets Theorem (Joint with Dibyendu 

De and Dona Strauss) 

Bart Kastermans (Wisconsin-Madison) 

Generating sets for cofinitary groups. 

Heike Mildenberger (Vienna) 

New partial orders with good Ramsay properities 

Arnold W. Miller (Wisconsin-Madison) 

The axiom of choice and the Borel hierarchy 

Bruce Sagan (Michigan State) 

Monotonic Sequence Games 

(Joint work with the Otago Theory Group) 

Andre Scedrov (Pennsylvania) 

Formal Analysis of Kerberos 5 Authentication Protocol 

Gary Weiss (Cincinnati) 

B(H)-Ideals: Recent Advances and Questions beyond Blass- 

Weiss 


Disturbances: Modelling Spread in Forests 

November 22–23, 2007 


Organizers: W. John Braun (Western), David Martell 

(Toronto), Charmaine Dean (SFU), Jim Gould (Ensis- 

CSIRO) 

A wave of inter-disciplinary activity involving mathematicians, 

statisticians, and forestry researchers is sweeping 

Canada. The Disturbances workshop was built on the successes 

of previous workshops on forestry and statistics held 

at Fields, BIRS, and SFU (PIMS). The earlier workshops 

were broadly based on forest fire science and ecology; Disturbances 

had a narrower focus: spread-modelling of fire 

and insects within forests. The support of MITACS allowed 

for valuable interactions with Australian researchers. 

The workshop initially focused on PROMETHEUS, the 

Canadian fire spread model. Cordy Tymstra emphasized 

the importance of accurately predicting forest fire spread to 

aid in the protection of homes and industries located in the 

wildland-urban interface. PROMETHEUS is a deterministic 

simulator based on the numerical solution of differential 

71


72 

“Thunder Bay # 37” a fire that occurred in May of this year 

Source: OMNR, Queen’s printer for Ontario, 2007 

equations derived from Huygens’ principle of wave propogation. 

Rates of spread are affected by topography, fuel 

type, and weather. A level set method is being considered 

for implementation. Rob Bryce described a contour tangle 

problem which has plagued PROMETHEUS. A topological 

solution was obtained following the 2006 PIMS Industrial 

Problem-Solving Workshop and is now operational. The 

principal behind that solution was Chris Bose who spoke 

on the qualitative behaviour of the solution of the PRO- 

METHEUS equations. Tanya Garcia described smoothing 

and bootstrapping the input data, yielding a stochastic version 

of the simulator. 

Kevin Tolhurst presented PHOENIX, the Australian model 

for fire spread. PHOENIX is based on the same physics as 

PROMETHEUS, but because of the spotting behaviour of 

Eucalyptus trees (which differs greatly from anything seen 

in Canada), more effort has been expended in modelling 

this kind of behaviour. Spotting is the generation of fires at 

new locations not connected with the main fire. 

Gail Ivanoff discussed the problem of optimal detection of 

a change-set in a spatial Poisson process. Application is to 

the spread of an airborne infection through a forest under a 

prevailing wind. Katherine Davies next described statistical 

inference for a spatial renewal process presented by Gail 

Ivanoff at the 2005 Fields workshop. Petro Babak presented 

fire propagation models based on temperature and fuel 

fraction, governed by a parabolic differential equation 

coupled to an ordinary differential equation. 

Data acquisition and analysis was discussed next. Doug 

McCrae described infrared techniques for fire spread 

data collection. Rob McAlpine discussed a fire behaviour 

knowledge data base which will make it easier for modellers 

to test new approaches. Sylvia Esterby applied some clustering 

methods to the problem of classifying historical fire 

weather patterns in order to identify more useful administrative 

fire weather zones. Doug Woolford continued on 

the theme of spatial data analysis, evaluating fire risk due 

to lightning and human causes using generalized additive 

models. Jim Gould discussed Australian fire behaviour. 

Two scientists from Western’s Boundary Layer Wind 

Tunnel gave talks on wind. Craig Miller described wind 

behaviour in response to topographical and roughness 

features on the landscape. Greg Kopp described how trajectories 

of wind-borne debris can be tracked and presented a 

possible application to the spotting of firebrands. 

The remainder of the meeting dealt with the spread of 

insects in forests. Rich Fleming described spruce budworm 

outbreaks in Eastern Canada and Ontario, and noted that 

there is as yet unexplained synchronicity; in an attempt to 

unravel this, he considered models of spread with and without 

contagion. Barry Cooke discussed the mountain pine 

beetle outbreak in British Columbia and Alberta, questioning 

the approaches that have been taken in displaying the 

data graphically. Marc Macias Fauria discussed a possible 

relationship between the Pacific Decadal Oscillation and 

mountain pine beetle populations and suggested that the 

presence of Arctic air entering the prairies will cause coldmortality 

events in Alberta which will prevent the beetle 

from spreading indefinitely. Bo Song and Sylvain Guichard 

presented models for insect spread in US, France and in 

Australia. 

Several coffee breaks which went overtime and a late 

night at Windermere Manor restaurant allowed for much 

discussion and interaction among many of the workshop 

participants. Several interdisciplinary research projects 

were spawned at this meeting; the exciting interface 

between forestry and the mathematical sciences is fertile 

ground for much future research activity. 


Petro Babak (Alberta) 

Differential equation models for forest fires 

Chris Bose (Victoria) 

Self similarity and Huygen’s principle

Rob Bryce (Brandon) 

v.5.x: An introduction to untangling 

Barry Cooke (Canadian Forest Service) 

Knocking on heaven’s door: modelling the spread of periodically 

eruptive forest insects attempting to invade climatically 

marginal habitats 

Katherine Davies (Western) 

Statistical behaviour of a spatial renewal process 

Sylvia Esterby (UBC-Okanagan) 

Classifying historical fire weather patterns 

Rich Fleming (Canadian Forest Service) 

Spread with and without contagion: the spruce budworm in 

Ontario as a case study 

Tanya Garcia (Neuchatel) 

Smoothing and bootstrapping the PROMETHEUS fire growth 

model 

Jim Gould (CSIRO) 

Fire in dry eucalypt forest: fuel structure, fuel dynamics and 

fire behaviour 

Sylvain Guichard (CSIRO) 

A tale of two pest spread models: a cellular automata population 

model, and a detailed individual-based model 

Gail Ivanoff (Ottawa) 

Optimal detection of a change-set in a spatial Poisson process 

Greg Kopp (Western) 

The aerodynamics of wind-borne debris: application to firebrands 

Marc Macias Fauria (Helsinki) 

Pacific decadal oscillation control of mountain pine beetle 

outbreaks in Western Canada 

Doug McCrae (Canadian Forest Service) 

Obtaining high-resolution data required for fire behaviour 

modelling 

Rob McAlpine (Ontario Ministry of Natural Resources) 

The fire behaviour knowledge base– a “third way out” 

Craig Miller (Western) 

Wind storms: Types, features, and modelling 

Bo Song (Clemson) 

The simulation of the southern pine beetle spot growth 


Kevin Tolhurst (Melbourne) 

Generalizing dynamic fire spread modelling–lessons from the 

development of PHOENIX 

Cordy Tymstra (Government of Alberta) 

Prometheus fire growth simulation model: Future directions 

Doug Woolford (Toronto) 

Exploring the seasonality of area burned by forest fires in 

Ontario 

John Braun 

Error-Control Codes, Information Theory and Applied 

Cryptography 

December 5–6, 2007 

Organizers: Aiden A Bruen (Calgary), David Wehlau (RMC 

and Queen’s) 

The old disciplinary barriers in Science and Engineering 

are breaking down at breakneck pace. This was never more 

evident than at this interdisciplinary conference which was 

organized as a kind of satellite meeting prior to the CMS 

Winter Meeting in London. The intention of the Fields 

conference was, in part, to attract participants to the CMS 

who would normally not attend a CMS meeting. The main 

goal, however, was to foster a productive but relaxed forum 

where broad themes would be treated, with ample time for 

discussion and networking. 

The conference was a great success. It covered current 

topics in biology (DNA codes), engineering and computer 

science (wireless networks and their capacity,VLSI design, 

error-control and space-time codes, radar), classical and 

quantum information theory, cryptography and also, of 

course, mathematics (MDS codes, perfect error-correcting 

codes, optical codes, random sequences). All of these topics 

integrated very nicely. 

It was wonderful to hear discussions involving DNA and 

Shannon entropy in the same breath, or to hear about the 

geometrical topic of Singer cycles being linked with topics 

in engineering such as pseudo random noise sequences and 

CDMA. The organizers received positive feedback from 

participants, in comments such as “you have performed a 

great service to the Science and Engineering communities.” 

On the non-technical side, the winter weather in Canada 

rose to the challenge. The weather in Toronto seemed 

unusually nippy. One hardy participant from British 

Columbia was surprised to learn that he would be spending 

the night in the always-glamorous confines of the airport 

73


in Edmonton but rallied splendidly to make the conference 

in good time for the reception. European participants, 

such as Olof Heden from KTH Stockholm seemed to have a 

smoother ride. 

On the Wednesday night, many of the conferenciers 

wended their way to Massey College where they dined, with 

appropriate pomp and ceremony, partaking of a Chanukahthemed 

meal in the company of the Master and Fellows of 

the College. The group, led by a former Junior Fellow, was 

warmly received by Master John Fraser. The organizers 

felt that the conclusion of the quotation from Santayana 

inscribed on the walls of the dining hall – to wit “To be 

happy you must be wise” – was particularly apt. Professor 

Heden was particularly interested to hear about the official 

visit of the King and Queen of Sweden, some months previously. 

Many of the group left for London on the Friday. 


Aiden Bruen (Calgary) 


Dmitry Trukhachev (Alberta) 

Multiple User Detection and Throughput of Ad-Hoc Wireless 

Networks 

Tony Macula (Geneseo College, SUNY) 

DNA codes 

Tim Alderson (UNB) 

Arcs and Optical Orthogonal Codes 

Robert Calderbank (Princeton) 

Space-Time Codes: Geometry versus Algorithms 

Olof Heden (KTH – Royal Institute of Technology, Stockholm) 

Perfect codes 

Michele Mosca (Institute for Quantum Computing (UW) 

and Perimeter Institute) 

Quantum information theory 

Vincent Gaudet (Alberta) 

Energy Efficient Decoding Algorithms 

David Wehlau 

Mini-symposium on Calculus of Variations in Physics, 

Geometry and Economics 

December 11, 2007 

Held at the University of Toronto 

Organizers: Robert McCann and Ben Stephens (Toronto) 

74 

Calculus of Variations has been a central and unifying 

tool in the fields of physics, geometry, and economics. Last 

December that theme was explored through a three day session 

at the Canadian Mathematical Society Winter meeting, 

capped by a one day Fields minisymposium. As many of the 

young speakers at the CMS meeting flew through Toronto, 

it was natural for them to stay over an extra day in Toronto 

to attend the minisymposium. Thanks to the funding of 

Fields and NSERC, this featured three leading researchers 

presenting recent progress in the fields. Together the events 

attracted researchers from a wide span of universities in 

Canada and the U.S. 

After early coffee in the math lounge, David Jerison kicked 

off the event with a talk referencing one of the oldest 

problems in Calculus of Variations: the minimal surface 

problem. We know from everyday life that soap-films 

minimize area by being smooth and saddle-shaped in the 

interior. This breaks down, however, in 8-dimensional 

space. Jerison presented a recently matured analogy 

between this phenomenon and phenomena in a free boundary 

problem which asks how to optimally mold a given 

quantity of insulation around a given shape of refrigerator 

to best protect it against warming. 

After a break for questions, Niky Kamran took to the 

blackboard, giving an impressively accessible and fluid 

introduction to the Penrose process. He sketched how 

black holes may split an incoming particle into one that is 

trapped and one that escapes, for a net export of energy. He 

then described the ingredients of a theorem (due to him 

and his collaborators) which rigorously treated a wave version 

of this process. 

At lunch young and old mixed in a nearby Chinatown 

restaurant. Then Bill Minicozzi closed out the day with a 

spirited and visually engaging overhead talk about widths 

and geometric flows. A basic and important question about 

mean curvature flow of surfaces in 3-space or intrinsic 

3-manifolds flowing by Ricci flow is: when do the manifolds 

disappear – when do they “go extinct?’’ It would be 

nice to estimate this time using geometric features of the 

manifold at the initial time. The width of a closed surface 

is the largest that a circle has to get to sweep out the surface 

once, starting from a point and ending at a point. By 

studying how this quantity changes with time, he and his 

longtime collaborator Colding were able to get sharp estimates 

for extinction time. 

We were pleased with the success of the event, drawing 25 

students and researchers. For junior members of the math

community, senior researchers can provide memorable, 

concrete examples of mathematical taste, vision, and fieldpropelling 

inspiration, as well as the opportunity to discuss 

our current challenges and achievements with sage voices, 

influential in the community. One favorite memory was 

hearing a postdoc ask Minicozzi to tell the story of how 

he began and maintained his collaboration with the nowsynonymous 

Colding. Another was a bit of history. Did you 

know the Lebesgue integral was invented by Lebesgue in his 

thesis, to help treat the minimal surface equation? 


David Jerison (MIT) 

Gradient bounds for a free boundary 

Niky Kamran (McGill) 

A rigorous treatment of energy extraction from a rotating 

black hole 

William Minicozzi (Johns Hopkins) 

The rate of change of width under flows 

Robert McCann 

Workshop in Asymptotic Group Theory and 

Cryptography 

December 14–16, 2007 


Organizers: Olga Kharlampovich (McGill) and Inna Bumagin 

(Carleton). 

The main theme of the workshop was the discussion of the 

trends in the infinite group theory motivated by cryptography. 

The workshop began in the morning on Friday, as had 

been planned, even though not all the participants from the 

USA and Europe were able to make it on time because of 

the snow storm. 

The first talk was given by Mark Sapir who started with 

a survey of known results about percolation in transitive 

graphs, then talked about joint work with Iva Kozakova 

about critical percolation on Cayley graphs of amalgamated 

products and HNN extensions, and finished by formulating 

some open problems related to percolation. Two survey 

talks were given by another main speaker, Tim Riley. In 

the first talk, he described outstanding problems in lowdimensional 

topology and group theory and some of their 

interconnections. His second talk focused on the geometry 

of the conjugacy problem in various classes of finitely 

presented groups and ended with a list of open problems. 

Vadim Kaimanovich (Bremen) showed in his talk how 

one can obtain the measure theoretical decomposition 


of the boundary of a free group, similar to the dynamical 

decomposition of the boundary corresponding to the 

group action. Alexei Miasnikov outlined a new geometric 

approach to free solvable groups which lead to a new upper 

bound for the complexity of the word problem, independent 

of the solvable length of a group. Free solvable groups 

were also discussed by C. K. Gupta whose talk was dedicated 

to sequences of test elements in free solvable groups. 

The test elements are used to determine whether a given 

endomorphism of a group is actually an isomorphism. 

Alexander Olshanskii explained a striking construction 

of a finitely presented group with non-quadratic Dehn 

function majorizable by a quadratic function on arbitrarily 

long intervals. Ilya Kapovich introduced several free group 

analogues of the curve complex and proved that they have 

infinite diameter, using an analogue of Bonahon “geometric 

intersection form.” Denis Osin used his version of 

the group theoretic Dehn surgery to prove some finiteness 

results about subgroups of Aut(G) with G being an arbitrary 

non-elementary relatively hyperbolic group. Zoran 

Sunic gave a characterization of groups of automorphisms 

of regular trees in terms of branch groups. Ben Steinberg 

gave a characterization of right-angled Artin groups with 

decidable problem of membership in rational subsets in 

terms of combinatorial properties of the associated graphs. 

Right-angled Artin groups were also discussed by Andrew 

Duncan who stated results about their universal theories; 

these results are applications of more general statements 

about universal theories of Stallings pregroups. Volker 

Diekert introduced a class of groups defined as Z[t]-completions 

of finitely generated groups and described their 

basic properties. The talk of Denis Serbin was dedicated to 

finite automata labeled by infinite words and their applications 

to algorithmic properties of groups. These techniques 

were also used to show that the index of a subgroup of a 

limit group in the ambient group or in the commensurator 

can be found effectively, as described by Andrey Nikolaev. 

Murray Elder proved in his talk that the Stallings group has 

a quadratic Dehn function. This best possible bound was 

achieved in joint work of several young mathematicians 

who were improving results of one another by introducing 

clever combinatorial tools. Dmytro Savchuk described 

two different constructions of graphs associated with the 

Thompson group F: one of these constructions leads to 

amenable graphs, while the other one gives non-amenable 

graphs. Vladimir Shpilrain explained how mathematicians 

can contribute to cryptography by designing authentication 

schemes which would be very hard to break. Francesco 

Mattucci showed an attack on the Shpilrain-Ushakov protocol 

for Thompson’s group F. 

75


Sponsors: 

The Fields Institute, Dean of Science and The School of 

Mathematics and Statistics, Carleton University 


(Talk titles not available) 

A. Miasnikov (McGill) 

V. Kaimanovich (International University Bremen) 

T. Riley (Cornell) 

M.Sapir (Vanderbilt) 

G. Bell (North Carolina, Greensboro) 

V. Diekert (Stuttgart) 

A. Duncan (Newcastle) 

R. Gilman (Stevens Institute) 

C.K. Gupta (Manitoba) 

S. Ivanov (UIUC) 

I. Kapovich (UIUC) 

A.Yu. Olshanski(Vanderbilt) 

D. Osin (CUNY) 

V. Shpilrain (CUNY) 

Z. Sunik (Texas A & M) 

Inna Bumagin 

Conference on Mathematical Physics and Geometric 

Analysis 

January 14–17, 2008 

Organizers: Tara Holm (Cornell), Yael Karshon (Toronto), 

Eckhard Meinrenken (Toronto), Chris Woodward (Rutgers) 

The core of this four-day meeting was two series of lectures 

by Victor Guillemin and Shlomo Sternberg, on topics straddling 

the borderline between mathematics and physics. 

Complementing these were 10 one-hour lectures, delivered 

by Anton Alekseev, Denis Auroux, Hans Duistermaat, 

Marco Gualtieri, Tamas Hausel, Richard Melrose, Reyer 

Sjamaar, Susan Tolman, Alejandro Uribe, and Steve 

Zelditch. The scope of the conference was deliberately 

broad, in order provide a perspective of the breadth of 

geometric analysis and its interaction with mathematical 

physics, and to stimulate discussion and collaboration 

between the 80 participants from different subfields. Topics 

were selected among recurring themes from the wide range 

of contributions by Guillemin and Sternberg. The conference 

thus served a secondary purpose to pay tribute to their 

long-lasting and successful collaboration. 

Shlomo Sternberg delivered three lectures on Internal 

supersymmetry and the standard model of elementary 

particle physics. Supersymmetry in particle physics refers 

76 

to a symmetry relating bosons and fermions, explaining 

patterns in the hierarchy of particles. After a detailed 

review of mathematical physics and Quillen’s theory of 

superconnections, Sternberg reported on his work with 

the late Yuval Ne’eman. In their 2005 paper, Ne’eman and 

Sternberg postulated that the u(2) gauge symmetry of the 

standard model of electroweak interactions is enhanced to 

a symmetry of the Lie superalgebra su(2|1). Their proposal 

is consistent with the experimental evidence of non-zero 

neutrino masses, and produces a ‘Weinberg angle’ that is 

fairly close to the experimentally observed value. Furthermore, 

it gives a concrete prediction of the mass of the (not 

yet observed) Higgs boson in terms of the mass of the W + - 

boson (observed in 1983). The Ne’eman-Sternberg theory 

will be put to test rather soon, since the Large Hadron Collider 

at CERN (which began operation in September 2008) 

is designed to operate at the required energy range. 

Victor Guillemin presented a survey of classical results 

and of some very recent progress on the subject of Birkhoff 

canonical forms. Guillemin reported that he himself had 

been introduced to the subject in Sternberg’s graduate 

course on celestial mechanics at Harvard, in 1961 (!). 

Guillemin’s first lecture, Theorems from Math I and Physics 

I revisited, described how to recover the shape of a 

1-dimensional potential from the spectral asymptotics of 

the Schrödinger operator. For general potentials, this question 

naturally leads to the idea of a semi-classical Birkhoff 

canonical form. Similar problems in higher dimensions 

constituted the subject of the second lecture, on Semi-classical 

Birkhoff canonical forms. Here, the spectral asymptotics 

involve not only the leading ‘Weyl asymptototics’ but 

additional contributions from the famous Gutzwiller trace 

formula for periodic orbits. Guillemin has demonstrated 

that the spectral data completely determine the quantum 

Birkhoff normal form along a periodic orbit. 

Eigenvalue asymptotics and semi-classical ideas played a 

key role in several of the one-hour talks at the conference. 

Alejandro Uribe described recent progress on eigenvalue 

clusters for the perturbations of the hydrogen atom and 

the asymptotics of zeroes of polynomials. Richard Melrose 

explained a ‘semi-classical proof’ of the odd Atiyah-Singer 

index theorem, and its extension to the ‘twisted’ index 

theorem of Mathai-Melrose-Singer. Steve Zelditch reported 

on some very recent work with Song and Rubinstein, using 

Kähler quantization to construct Monge-Ampère geodesics. 

Starting with notions from elementary geometry, Hans 

Duistermaat explained the notion of a QRT transformation, 

a certain analytic diffeomorphism of an elliptic curve.

eckhard Meinrenken, yael Karshon, Tara holm, 

Sylvie paycha and Shlomo Sternberg 

He explained how these may be viewed as symplectic 

4-manifolds with singular Lagrangian fibrations. Marco 

Gualtieri lectured on 4-manifolds, equipped with symplectic 

structures which ‘blow up’ along submanifolds and 

give rise to complex structures along the blow-up loci. His 

constructions involved Dirac geometry, as did Anton Alekseev’s 

discussion of ‘pure spinors’ on Lie groups. Alekseev 

explained how his construction (in joint work with Bursztyn 

and Meinrenken) gives a new perspective on the theory 

of quasi-Hamiltonian group actions. 

Reyer Sjamaar spoke on joint work with Holm on integral 

equivariant cohomology, and the use of divided differences 

operators in this context. Sue Tolman gave an introduction 

to her work with Goldin and with Sabatini on effective 

calculations in equivariant Schubert calculus, revisiting 

a result of Guillemin and Zara. Tamás Hausel discussed 

work with Proudfoot on the geometry and topology of toric 

hyper-Kähler varieties and quiver varieties. In the final lecture, 

Denis Auroux demonstrated how ideas coming from 

string theory, such as the notion of mirror symmetry, are 

employed to study moduli spaces of Lagrangian submanifolds 

in Kähler manifolds. 

Notes for Guillemin’s and Sternberg’s lectures, as well as 

slides and audio files of the invited talks, are available 

on the Fields Institute website, www.fields.utoronto.ca/ 

programs/scientific/07-08/geomanalysis/ In addition to 

the more formal lectures, Megumi Harada and Tara Holm 

presented a melodic summary of equivariant geometry 

titled `Ode to Victor and Shlomo,’ posted on YouTubeTM at 

www.youtube.com/watch?v=vmfT1l83CM4 




Anton Alekseev (Geneva) 

Denis Auroux (MIT) 

Hans Duistermaat (Utrecht) 

Marco Gualtieri (MIT) 

Victor Guillemin (MIT) 

Tamas Hausel (Oxford) 

Richard Melrose (MIT) 

Alejandro Uribe (Michigan) 

Shlomo Sternberg (Harvard) 

Reyer Sjamaar (Cornell) 

Susan Tolman (UIUC) 

Steve Zelditch (Johns Hopkins) 

Eckhard Meinrenken 

First Canada-Mexico Statistics Meeting 

February 22–23, 2008 

Held at the Center for Research in Mathematics (CIMAT), 

Guanajuato, Mexico 

Organizers: Statistical Society of Canada/ Societé statistique 

du Canada, Aurélie Labbe(Laval), Richard Lockhart (SFU), 

Salomón Minkin (Ontario Cancer Institute), Román 

Viveros-Aguilera (McMaster), Asociación Mexicana de 

Estadística (Mexican Statistical Association), Eduardo 

Castaño (Universidad Autónoma de Querétaro), Graciela 

González Farías (Centro de Investigación en Matemáticas, 

AC), Eduardo Gutiérrez (Instituto de Investigaciones en 

Matemáticas Aplicadas y en Sistemas, UNAM), Manuel 

Mendoza Ramírez (Instituto Tecnológico Autónomo de 

México) 

This conference’s long-term objective was to foster research 

interactions, collaborations and graduate student training 

between the statistical communities of Canada and Mexico. 

The meeting built on a number of successful previous and 

current research efforts leading to joint projects and publications, 

and training of graduate students involving the two 

countries. The meeting was a joint effort of the Mexican 

Statistical Association and the Statistical Society of Canada, 

the main sponsors. 

The number, 114, of registered participants, exceeded our 

prior estimate of about 100. In total, 25 Canadians participated, 

including senior and young researchers as well 

as graduate students. The conference featured 7 plenary 

talks, 25 invited presentations and 28 contributed poster 

presentations. Our colleagues Jim Ramsay, Nancy Reid and 

David Sprott were among the plenary speakers. All sessions 

77


78 

Conference organizers Roman Viveros- aguilera, 

Rosy Davalos and Graciela Gonzales-Farias 

were very well attended and the presentations from both 

sides were noted for their high quality. The topics covered 

ranged from the very applied modern areas of functional 

data modeling and analysis, financial statistics, survey sampling 

and statistical genetics to fancy theories of likelihood 

and Bayesian methods. The complete program is posted at: 

www.cimat.mx/Eventos/canada-mexico-SM/ 

The friendly atmosphere allowed for a good deal of interaction 

at coffee breaks and lunches. The poster session was 

very well attended and a lot of feedback was passed onto 

the presenters who were mostly young statisticians. This 

fulfilled one of the conference’s objectives. 

There were also opportunities for interactions at professional 

levels. A pleasant lunch meeting between the 

Mexican Statistical Association and the Statistical Society 

of Canada Executive Committees took place where 

information was exchanged about our societies and ideas 

discussed on future joint ventures. It was agreed to consider 

organizing a follow-up meeting in about two years, likely in 

a Canadian location. Jamie Stafford promoted our National 

Institute on Complex Data Structures at a meeting with 

members of the Executive Committee of the Mexican Statistical 

Association, including their President. Specifically, 

Mexican statisticians were invited to consider making joint 

submissions with Canadians on research ventures of common 

interest. 

We were very pleased to receive sponsorships from Fields 

Institute, the Pacific Institute for the Mathematical Sciences 

and the National Program for Complex Data Structures. 

The Mexicans were very active in raising funds from their 

National Council of Science and Technology to support 

participation of their young statisticians, including a good 

number of graduate students, as well as from a variety 

of companies including beer and tequila producers. The 

CIMAT leaders were very supportive of the meeting, specifically 

on logistics and secretarial support, in addition to 

providing the venue for the meeting. 

Thanks to the photographic efforts of the Dean-Hall 

family, there are about 53 pictures from the conference 

posted at: www.flickr.com/photos/ssc_liaison/ 

sets/72157604061341167/ 

We thank the Fields Institute for its generous monetary 

support which helped to partially fund the invited speakers, 

and also the Canadian and Mexican speakers and organizers 

who made it all possible. 


Jim Ramsay (McGill) 

Parameter Cascading for High Dimensional Models 

Jason D. Nielsen (Carleton) 

Adaptive Spline Models for the Analysis of Recurrent Event 

Panel Data 

Eduardo Castaño (Universidad Autónoma de Querétaro) 

Functional Linear Models: Applications and Test of Hypotheses 

Dave Campbell (SFU) 

Estimating Parameters from Differential Equation Models 

Reg Kulperger (Western) 


Begoña Fernández Fernández (Facultad de Ciencias, 

UNAM) 

Estimation of Value at Risk and Ruin Probability for Diffusion 

Processes with Jumps 

Jeffrey S. Rosenthal (Toronto) 

Adapting the Metropolis Algorithm 

Víctor Pérez-Abreu (Research Center of Mathematics, 

Guanajuato) 

On Random Matrices and Dyson Brownian Motion 

Christian Genest (Laval) 

Goodness-of-fit Tests for Copula Models: The State of the Art 

José Luis Batún Cutz (Universidad Autónoma de Yucatán) 

and Javier Rojo (Rice) 

Estimation of Symmetric Distributions Subject to a 

Peakedness Order 

Jamie Stafford (Toronto) 

Local Likelihood and the EMS Algorithm

Ernesto Barrios (ITAM) 

Bayesian Factor Screening and MD-optimal Design 

Bovas Abraham (Waterloo) 

Business and Industrial Statistics: A Historical Perspective 

Víctor Aguirre (ITAM) 

Bayesian Detection of Active Effects in Designed Experiments 

Modeled with GLM’s 

David Sprott and Eloísa Díaz-Frances (Research Center of 

Mathematics, Guanajuato) 

Thinking in Terms of Likelihood 

Alfredo Bustos y de la Tijera and Luis Angel Rodríguez Silva 

(Aguascalientes) 

Comparative Analysis of the Conditional Poisson Sampling 

and a New Alternative Scheme of Sampling of Sequences 

of Independent and Identical Distributed Draws (Draw by 

Draw) 

Adán Díaz Hernández (ITESM-CCM, Monterrey) 

An Economic Capital Model for Credit Risk using Generalized 

Elliptical Copulas and Extreme Value Theory 

Addy M. Bolivar, E. Díaz-Francés, and J. Ortega (Research 

Center of Mathematics, Guanajuato) 

Bootstrap Intervals for Estimating Quantiles of Asymptotic 

Distributions of Maxima 

Angélica Hernández Quintero (Universidad Autónoma 

Metropolitana, Iztapalapa), Jean-François Dupuy (Université 

Toulouse 3), Gabriel Escarela (Universidad Autónoma 

Metropolitana, Iztapalapa) 

A Semiparametric Model for the Analysis of Competing Risks 

Data 

Antonio Alonso Aréchar (Ministry of Economic Development, 

State of Aguascalientes) 

Education expenditure of the Mexican family: Does cognitive 

ability matter 

Carlos Cuevas Covarrubias (Anáhuac University) 

Principal Componentes and ROC Curves 

Elizabeth González Estrada, José A. Villaseñor Alva (Colegio 

de Postgraduados, Texcoco) 

A Generalization of Shapiro-Wilk’s Test for Multivariate 

Normality 

Elizabeth Juárez (SFU) 

Modeling Growth Curves for Lodgepole Pines 

Eunice Campirán García (IIMAS-UNAM, Mexico City) 

Detecting Cervical Cancer with Bayesian Nonparametric 

Statistics 


Félix Almendra Arao and David Sotres Ramos (Colegio de 

Postgraduados, Texcoco) 

About the Barnard Convexity Condition for Non-inferiority 

Tests 

Fidel Ulin-Montejo(UJAT, Cunduacán. Tabasco/Colegio 

de Postgraduados, Montecillo) and Humberto Vaquera- 

Huerta (Colegio de Postgraduados, Montecillo) 

Comparison of Mean Pollutant Concentrations of Lognormal 

Populations Containing Nondetects Data 

Francisco J. Ariza-Hernández (Colegio de Postgraduados, 

Texcoco) and Gabriel A. Rodríguez-Yam (Universidad 

Autónoma Chapingo) 

Risk process with stochastic volatility 

Gerardo Rubio Hernández (UNAM), Héctor Lamadrid- 

Figueroa (National Institute of Public Health, Cuernavaca) 

Use of Errors-in-variables Regression Models for Studies with 

KXRF Bone Lead Measurements: Comparison to OLS with a 

Simulation Based Approach 

Hortensia J. Reyes Cervantes (FCFM-BUAP-Colegio de 

Postgraduados) and Humberto Vaquera Huerta (Colegio de 

Postgraduados, Montecillo) 

Estimation of Trends in the Very High Levels of Urban Ozone 

by Using the Generalized Extreme Value Distribution 

JC Loredo-Osti (Memorial) 

A Graph Theory Approach to Pedigree Likelihood 

Jorge Argaez and E. Pech (Yucatán) 

A Statistical Approach for the Algorithm Domain: Estimation 

of Species High Potential Distribution Area 

José A. Montoya, Eloísa Díaz-Francés, David A. Sprott 

(Research Center of Mathematics, Guanajuato) 

On a Criticism of the Profile Likelihood Function 

Leonardo Román Olmedo García, Alberto Castillo Morales 

(Universidad Autónoma Metropolitana- Iztapalapa, Mexico 

City) 

Test of a Compound Central Null Hypothesis and a Bilateral 

Alternative Hypothesis in the Normal Distribution 

Lorelie Hernández Gallardo and Gabriel Escarela (Universidad 

Autonoma Metropolina, Iztapalapa, Mexico City) 

An Extreme Value Model for Environmental Time Series: An 

Application to Ground-Level Ozone Data Analysis 

Nelson Omar Muriel Torrero (UNAM) 

EVT for the Multivariate Garch Model with Constant Conditional 

Correlations 

79


Paulino Pérez Rodríguez and José A. Villaseñor Alva (Colegio 

de Postgraduados, Montecillo) 

Bayesian Inference for the Skew Normal Distribution 

Sigfrido Iglesias-Gonzalez (University of Toronto / 

Research Center of Mathematics, Guanajuato) 

Highly Accurate Tests for the Mixed Linear Model 

Meteorologically-dependent and Non-stationary Trends in 

Tropospheric Ozone: A Bivariate Extreme Analysis 

Tania Moreno Zúñiga and Gabriel Escarela Perez (Universidad 

Autónoma Metropolitana, Iztapalapa), Víctor Muñiz 

Sánchez, Rogelio Ramos Quiroga and Johan Van Horebeek 


Feature Selection on Kernel PCA 

Víctor Ignacio López Ríos (Universidad Nacional de 

Colombia, sede Medellín) and Rogelio Ramos Quiroga 


Optimum Designs for the Dual-Problem Discrimination and 

Nonlinear Functions Estimation for a Compartmental Model 

and Optimal Augmentation of Two-level Orthogonal Arrays 

Victorino Morales Ramos (Colegio de Posgraduados, Texcoco) 

Wayne Nelson (Consultant Schenectady, New York) 

Comparison of Entire Mean Cumulative Functions of Sets of 

Recurrence Data 

Manuel Mendoza Ramírez (ITAM) 

Bayesian Risk Analysis 

Víctor Guerrero Guzmá (ITAM and INEGI) 

Estimating Trends with Percentage of Smoothness Chosen by 

the User 

Cody Hyndman (Concordia) 

Forward-Backward Stochastic Differential Equations and 

Term Structure Derivatives 

Luis G. González, Graciela González-Farías and M. Vittoria 

Levati (Max Planck) 

Logit Estimation of Conditional Cooperation in a Repeated 

Public Goods Experiment 

Claudia Rangel (National Institute of Genomic Medicine) 

Dynamic Modeling of Gene Expression Data 

Shelley B. Bull (Mount Sinai Hospital and Toronto) 

Statistical Genetic Methods: Issues in Genome-wide Complex 

Trait Studies 

80 

Arturo Becerra (UNAM) 

Detection of horizontally transferred genes using a first-order 

Markov models 

Nancy Reid (Toronto) 

Weighting the Likelihood Function 

Richard Cook (Waterloo) 

Analysis of a Non-Susceptible Fraction with Current Status 

Data 

Belem Trejo-Valdivia (National Institute of Public Health, 

Cuernavaca) 

Statistical Issues in Evaluation Research 

Charmaine Dean and Darby Thompson (SFU) 

Mixture Models in Multi-Phase Survival Analysis” 

Subhash R. Lele, Monica Moreno and Erin Bayne (Alberta) 

Site Occupancy and Detection Error: What Can We do With 

a Single Visit? 

Jiahua Chen (UBC) 

Asymptotic Normality under Two-Phase Sampling Designs 

José Elías Rodríguez (Guanajuato) 

Improving the Precision in Survey Sampling 

N.G. Narasimha Prasad and Subhash Lele (Alberta) 

Robust Model Prediction for Small Areas 

Federico O’Reilly Togno (IIMAS/UNAM) 

On the cone algorithm 

Fernando Avila Murillo (Consultant for the tequila industry, 

Research Center of Mathematics, Guanajuato) 

Mexican Tequila 

Roman Viveros-Aguilera 

Waterloo Workshop on Computer Algebra 


Held at Wilfrid Laurier University 

Organizers: I. Kotsireas and E. Zima (Wilfrid Laurier) 

The Second WWCA was hosted by the CARGO lab at WLU, 

and was dedicated to the Russian mathematician Georgy 

Egorychev from Krasnoyarsk, on the occasion of his 70th 

birthday. He is well known as the author of the influential, 

milestone book Integral Representation and the Computation 

of Combinatorial Sums, in which a regular approach 

to combinatorial summation, also known nowadays as the 

method of coefficients, is described. Another of Egorychev’s

notable achievements is his solution in 1980 of the celebrated 

van der Waerden conjecture on the determination of 

the minimum of the permanent of doubly stochastic matrices 

for which he was awarded the D. R. Fulkerson Prize. A 

CD with his selected works, including the fruit of 27 years 

of research on permanents – a new book on permanents – 

was distributed to all participants of the workshop. 

The topics discussed at the workshop were closely related 

to these two themes – combinatorial and algorithmic summation 

and special polynomials – and related problems in 

enumerative combinatorics and graph theory. The format 

of the workshop included invited lectures and contributed 

presentations. The workshop attracted speakers from Canada, 

USA, Europe and Taiwan and participants from WLU, 

Waterloo, Toronto, Guelph, and other Ontario universities. 

Different aspects of the method of coefficients, its relation 

to algorithmic summation methods and methods of proving 

combinatorial identities were thoroughly discussed by 

George E. Andrews, Georgy Egorychev, Ira Gessel, Angèle 

Hamel, I-Chiau Huang, Peter Paule, Marko Petkovsek, 

Doron Zeilberger and Eugene Zima. 

The theory and applications of the permanent and other 

special polynomials were lectured on by Leonid Gurvits, 

Ilias Kotsireas and Herbert Wilf. 

New results in graph theory were presented by Kathie Cameron 

and Chinh Hoang. 

Michiel Hazewinkel discussed the “niceness” of mathematical 

objects and theorems. 

Many interesting (and sometimes heated) discussions on 

the interactions between Combinatorics, Algebra, and 

Graph Theory, took place during the workshop question 

periods. Participants enjoyed these discussions as much as 

they did the well-presented lectures. 

The success of the local organization was largely due to 

volunteer students from WLU “Φ club”. 

This conference would not have been possible without the 

generous financial support of the Fields Institute for which 

the conference organizers are very grateful. The conference 

also received financial support from internal WLU sources. 


Georgy P. Egorychev (Krasnoyarsk) 

The method of coefficients: applications in ring theory and the 

Collatz problem 


George Andrews(Penn State) 

Old and New Thoughts on the Rogers-Ramanujan Identities 

Ira Gessel (Brandeis) 

The Method of Coefficients 

Leonid Gurvits (Los Alamos National Laboratory) 

Van der Waerden/Schrijver-Valiant like Conjectures and 

Stable (aka Hyperbolic) 

Michiel Hazewinkel (CWI) 

Niceness theorems 

I-Chiau Huang (Taiwan) 

Power series, differentials and residues 

Peter Paule (RISC, Johannes Kepler University Linz, Austria) 

Combinatorial Multi-Sums: Algorithmic Approaches from 

Egorychev to WZ 

Marko Petkovsek (Ljubljana) 

Subanalytic hypergeometric and P-recursive summation 

Herbert Wilf (Pennsylvania) 

The permanent importance of the permanent function 

Doron Zeilberger (Rutgers) 

Integral Representations from Euler to Egorychev 

Ilias Kotsireas 

Prairie Network Conference and Workshop 


Held at Brandon University 

Organizers: Murray Bremner (Saskatchewan), Douglas 

Farenick (Regina), Chenkuan Li (Brandon), Anna Stokke 

(Winnipeg), Nina Zorboska (Manitoba) 

The GRACE (Geometry, Representation theory, Algebraic 

Combinatorics and Epidemiology) Workshop was a 

wonderful success and the event attracted many female 

undergraduates and graduates from Regina and Winnipeg. 

The workshop was aimed at senior undergraduates and 

beginning graduate students. Its objective was to convey a 

flavour of research-level mathematics to the students, and 

to encourage them to consider an academic career in mathematics. 

In addition to the four one-hour presentations, the 

workshop provided an opportunity for young researchers 

and faculty at prairie universities to meet face-to-face and 

discuss issues and initiatives related to the network. The 

participants’ comments on the workshop were very enthusiastic 

and great appreciation was shown for the Question 

81


and Answer Session, held at the end of the workshop for 

an hour and a half, 30 minutes longer than planned. Many 

thanks go to Jaydeep Chipalkatti and Anna Stokke for organizing 

a successful event! 

The Annual Meeting was also highly successful, held in an 

open and casual atmosphere: interesting talks were made 

on a wide range of topics that are particularly relevant to 

the socio-economic needs of the provinces of Manitoba and 

Saskatchewan. All attendees appreciated the hospitality of 

Brandon University, and the local organizing committee 

members, Chenkuan Li and Jeff Williams. Vice President 

Scott Grills welcomed all participants and Dean Austin 

Gulliver, Faculty of Science, attended the conference banquet 

and gave a warm speech. 

Anna Stokke, Steve Kirkland and Chenkuan Li met briefly 

to discuss the future of the Prairie Network. They agreed 

that the Annual Meeting is a positive, intellectually stimulating 

event for the PNRMS to continue and that a Student 

Workshop associated with the Annual Meeting would be 

a valuable addition to the Network’s activities. Regarding 

next year’s Annual Meeting, the Network had already 

planned to have it at the University of Saskatchewan. 

Financial support was provided by the Fields Institute, 

PIMS and the CMS. 


Shaun Fallat (Regina) 

Applications of total positivity 

Stephanie Portet (Manitoba) 

Mathematical modeling of the cytoskeleton 

Michael Kozdron (Regina) 

A random look at the Schramm-Loewner evolution 

Eric Schippers (Manitoba) 

Quasiconformal Teichmueller theory 

Anna Stokke (Winnipeg) 

Quantum Schur algebras and Desarmenien matrices 

Salma Kuhlmann (Saskatchewan) 

Approximation of positive polynomials by sums of squares 

Morten Nielsen (Queen's) 

A cycle partition problem for graphs 

Chenkuan Li (Brandon) 

A review of products of distributions 

Murray Bremner (Saskatchewan) 

Structure constants for the enveloping algebra of the fivedimensional 

non-Lie Malcev algebra 

82 

Michael Roddy (Brandon) 

Algorithmic approaches to the product problem for the infinite 

case 

Vaclav Linek (Winnipeg) 

New results on polyhedral designs 

Jaydeep Chipalkatti (Manitoba) 

On equations defining coincident root loci 

Mikhail Kotchetov (Manitoba) 

Group gradings on simple Lie algebras 

Remus Floricel (Regina) 

E 0 -semigroups on von Neumann algebras 

Chenkuan Li 

Workshop on Mathematical Modeling and Analysis of 

Wireless Networks 

May 8-9, 2008 

Organizers: Jorg Liebeherr (Toronto), Peter Marbach 

(Toronto), Ravi Mazumdar (Waterloo), Catherine Rosenberg 

(Waterloo) 

Mathematical models play an important role in the understanding 

and control of wireless computer networks. They 

enable one to obtain insight into how networks and traffic 

are formed, as well as how to design mechanisms and 

algorithms to efficiently transmit information. Mathematical 

models are also an essential tool in understanding the 

fundamental performance limits and trade-offs in wireless 

networks. As the network infrastructure changes and 

new applications emerge, the mathematical models need 

to evolve as well. The workshop explored recent developments 

in mathematical modeling and analysis of wireless 

networks in areas such as network coding, cellular wireless 

networks, wireless ad hoc and mesh networks, and cognitive 

radio. 

A total of 12 external invited speakers presented talks 

ranging from fundamental modeling based on random 

graphs to models that predict throughput of contention 

based protocols for MAC and experimental observations on 

the behavior of TCP algorithms over multi-hop networks. 

The papers were of various types and the speaker profiles 

ranged from budding researchers to well known leaders of 

the field. The underlying commonalities were the role of 

mathematical models and tools. 

Some of the key mathematical tools presented were on 

percolation and random graph models and extensions

of classical Erdos-Renyi models, continuum percolation, 

Markov processes, stochastic approximation and MCMC. 

Some talks were on recent results whereas others were of 

overviews The workshop format allowed for ample discussion. 

The participants were drawn from the ranks of graduate 

students from the local as well as other Canadian Universities 

as well as faculty from McGill, McMaster, Alberta and 

UBC. The attendence was capped at 60 and was oversubscribed. 

Representatives of industrial partners Nortel, Bell, 

RIM, and GM also attended. 

In addition to the regular workshop there was a conference 

reception and dinner held that was well received and greatly 

appreciated by all. They were impressed by the facilities 

at Fields and they also got a chance to sample the simple 

delights of walking around the lovely surroundings of the U 

of T campus and Toronto’s Chinatown on two lovely spring 

days. 

The feedback we received was extremely positive about 

the technical level, and there was a request to make this a 

regular event! 

Invited Speakers: (as listed on program itinerary) 

Sem Borst (Alcatel-Lucent Bell Labs and Eindhoven Univ. 

of Techology) 

Some distributed resource sharing and scheduling problems in 

wireless networks 

Ed Knightly (Rice) 

Modeling and experimental validation of multi-hop wireless 

networks 

Vikram Krishnamurthy (UBC) 

Global games and correlated equilibria for decentralized 

spectrum access 

Armand Makowski (Maryland) 

Intersecting random graphs 

Laurent Massoulie (Thomson Research) 

Content popularity and user profiling for content placement 

in peer-to-peer VoD systems 

Mike Neely (USC) 

Dynamic data compression for wireless transmission over a 

fading channel 

Alexandre Proutiere (Microsoft Research) 

Scheduling mobile users in wireless networks 

Devavrat Shah (MIT) 

On capacity scaling in arbitrary wireless networks 


Ness Shroff (OSU) 

Optimizing energy efficiency for sleep-wakeenabled sensor 

networks using "anycasting" 

Patrick Thiran (EPFL Lausanne) 

Fairness, spatial reuse and phase transition in 802.11 networks 

Jean Walrand (Berkeley) 

A distributed algorithm for optimal throughput and fairness 

in wireless networks with a general interference model 

Edmund Yeh (Yale) 

Information dissemination in mobile wireless networks. 

Peter Marbach 

Ottawa-Carleton Discrete Mathematics Days 



Organizers: Brett Stevens and Qiang (Steven) Wang (Carleton) 

The Ottawa-Carleton Discrete Mathematics Days 2008, 

sponsored by the Fields Institute and followed by the 

Ottawa-Carleton graph theory workshop, was held at 

Carleton University on May 9 and 10. It brought together 

many researchers, graduate students, and postdoctorial 

fellows from across Ontario, Canada and the world. This 

event consisted of five 1-hour-long invited lectures and six 

30-minute-long contributed talks. This workshop allowed 

a great exchange of ideas and promoted talks by researchers 

at different stages of their career, including talks given by 

graduate students. 

There were two invited lectures and four contributed talks 

on the first day. In the first lecture, Ortrud R. Oellermann 

surveyed characterizations of graph classes that possess 

several local convexities. Her lecture concluded with some 

new results and open problems. The second lecture, given 

by Qing Xiang, was on symplectic analogues of Hamada’s 

formula for the p-rank of the incidence matrix between 

1-flats and m-flats of symplectic polar space Sp(2m,q). 

The history of the problem and a very nice closed formula 

for the p-rank of the incidence matrix between the points 

and lines of symplectic polar space Sp(4,q) were presented. 

Four contributed talks covered topics including graph 

decomposition, hypergraphs, and design theory. The first 

day ended with a nice reception (thanks to the staff support 

from the School of Mathematics and Statistics at Carleton 

University). 

83


The second day consisted of three invited lectures and two 

contributed talks. Bruce Shepherd presented several models 

for designing a network when the traffic demand is either 

unknown in advance or will be rapidly changing. The difficult 

issues caused by extra flexibility were discussed. David 

Bremner described the duality between maximal separation 

and minimal distance and discussed a generalization of 

the duality to an arbitrary Minkowski metric and to the 

inseparable case. Ian Goulden surveyed some recent work 

on the enumeration of maps (graphs embedded on a surface 

of arbitrary genus) and branched covers of the sphere and 

discussed various results and methods including several 

methods from mathematical physics. The day concluded 

with two contributed talks on computational issues related 

to random graphs and digraphs respectively. 

The event was successful in bringing together people working 

in various fields of Discrete Mathematics across Ontario 

and beyond. The talks this year covered a wide range of topics 

including combinatorial optimization, network flows, 

enumeration, graph theory, designs and finite geometry. 

Invited Speakers: (as listed on program itinerary) 

Ortrud R. Oellermann (Winnipeg) 

Graph classes characterized by local convexities 

Qing Xiang (Delaware) 

Symplectic analogues of Hamada’s formula 

Bruce Shepherd (McGill) 

Robust optimization of networks 

David Bremner (Technische Universität München) 

The duality between maximal separation and minimal distance 

Ian Goulden (Waterloo) 

Maps and branched covers – combinatorics, geometry and 

physics 

Brett Stevens 

Ottawa-Carleton Graph Theory Workshop 2008 



Organizers: Kevin Cheung (Carleton), Jason Gao (Carleton), 

and Mateja Šajna (Ottawa) 

The workshop brought together over 50 participants from 

across Ontario, Canada and abroad, including 30 students 

and postdoctoral fellows. The response to the call for 

84 

contributed talks was overwhelming. In addition to the 

five one-hour invited lectures, the two-and-a-half-day 

workshop had eleven 25-minute contributed talks. The 

workshop provided a great opportunity for students and 

researchers at different stages of their career to exchange 

ideas and present their research. 

Xingxing Yu gave the first lecture, and spoke on recent 

work on judicious partitions of graphs. On the second day, 

Michel Goemans talked about two recent results on finding 

minimum-cost spanning tree with bounded degree that 

use different techniques. Charlie Colbourn’s lecture began 

the afternoon session, on the subject of graph decompositions 

and optimal grooming with applications in optical 

networking. 

On the final day, Bruce Reed described a recent result 

on the fractional chromatic index obtained using linear 

programming, the probabilistic method, and graph decomposition. 

Penny Haxell gave a common generalization of 

Scarf’s Lemma and Sperner’s Lemma and used Scarf’s 

Lemma to show that the Stable Paths Problem, which is an 

abstraction of a network routing problem concerning the 

Border Gateway Protocol (BGP) and could fail to have a 

solution, always has a fractional solution. 

The event was a great success in bringing together people 

working in graph theory across Ontario and beyond. The 

talks this year covered both theoretical results and applications 

of graph theory. 


Charlie Colbourn (Arizona State) 

Graph decompositions and optimal grooming 

Michel X. Goemans (MIT) 

Minimum bounded degree spanning trees 

Penny Haxell (Waterloo) 

Scarf’s lemma and the stable paths problem 

Bruce Reed (McGill) 

Graph colouring à la Chvatal 

Xingxing Yu (Georgia Tech) 

On judicious partitions of graphs 

Kevin Cheung

Workshop on Topological Methods in Algebra, Analysis 

and Dynamical Systems 


Held at Nipissing University 

Organizers: Nikolay Brodskiy (Tennessee), John C. Mayer 

(Alabama), Vladimir Pestov (Ottawa), Alexandre Karasev 

(Nipissing), Murat Tuncali (Nipissing), Vesko Valov 

(Nipissing) 

The workshop comprised 17 one-hour lectures, of which 

all but one were live video-streamed; they were watched 

through the internet at various sites in Europe, Asia and 

Australia (and can be seen at www.nipissingu.ca/topology). 

Participants came from Canada, the US, Cameroon, 

Colombia and Japan. 

The workshop provided the opportunity for recently 

trained professional mathematicians and students to prepare 

for research in areas in which current developments 

are moving rapidly at the intersection point of topology, 

analysis, algebra, and dynamics. Major speakers of international 

repute, who are active in these research areas, 

devoted a significant amount of their time to working with 

students. 

The first part of the workshop featured lectures by Vladimir 

Uspensky, Benoit Collins, Stefano Ferri, and Gabor 

Lukacs. Uspensky’s lectures were on topological dynamical 

systems and their enveloping topological semi-groups. By a 

topological dynamical system, we mean a pair (G,X) where 

G is a topological group acting continuously on a compact 

space X. Uspensky’s talk surveyed results which show the 

interplay between Banach spaces, topological semigroups 

and dynamical systems. Benoit Collins gave two lectures 

on Weingarten calculus, which gives a general method of 

computing integrals over compact matrix groups. Stefano 

Ferri’s lectures concentrated on topological centers arising 

in various algebras studied in harmonic analysis. Gabor 

Lukacs delivered lectures on rings of continuous functions 

and their applications in the study of locally precompact 

groups. 

workshop on Topological Methods participants 


The last three days of the workshop were devoted mainly to 

complex dynamics and plane topology. Featured speakers 

were Bob Devaney, Jane Hawkins, Lex Oversteegen, Judy 

Kennedy, Kazuhiro Kawamura, and John Mayer. Bob Devaney 

gave a series of very well received lectures on complex 

dynamics and complex topology focusing on rational functions, 

which are singular perturbations of polynomials, and 

surveying recent results and open questions. Jane Hawkins 

spoke about elliptic functions and the topology of their 

Julia sets. Lex Oversteegen talked on geometric methods 

for plane continua with applications to extending isotopies. 

Judy Kennedy spoke on applications of inverse limits to 

backward-in-time economic models. Kazuhiro Kawamura 

discussed some counter-intuitive examples in the homology 

and homotopy theory of spaces related to the Hawaiian 

earring. John Mayer spoke on a recent proof of the Makienko 

Conjecture for rational functions whose Julia set is a 

decomposable continuum. 

There were 21 graduate students and recent PhDs and 8 

senior undergraduate students participating. On each day 

of the workshop, an hour-long special question-and-answer 

session was held for students, and speakers were invited 

to these sessions to answer questions. The intention was 

to provide a more comfortable forum to ask questions of 

speakers. These sessions allowed students to find out more 

about elementary topics which are typically familiar to the 

experts (and for which an inhibition about asking in the 

context of a talk might exist). Nearly all of the speakers participated 

in these student sessions. Several of the speakers 

were very forthcoming on answering students’ questions, 

even outside their own area of expertise. 

In addition to the funding from the Fields Institute, the 

National Science Foundation provided funding for US 

based graduate students, recent PhDs and advanced undergraduate 

students, to participate in the workshop. 



Benoit Collins (Ottawa) 

Robert L. Devaney (Boston) 

Jane M. Hawkins (North Carolina at Chapel Hill) 

Kazuhiro Kawamura (Tsukuba University) 

Judy Kennedy (Lamar) 

Gabor Lukacs (Manitoba) 

Matthias Neufang (Carleton) 

Lex Oversteegen (Alabama-Birmingham) 

Vladimir Uspensky (Ohio, Athens) 

Murat Tuncali 

85


Workshop on Around Connes’ Embedding Problem 



Organizers: Benoit Collins, Thierry Giordano, 

David Handelman and Vladimir Pestov (Ottawa) 

Scientific Advisory Committee: George Elliott (Toronto), 

Roland Speicher (Queen's) 

The question currently known as the Connes embedding 

problem (CEP), arose in a 1976 paper of Connes in which he 

asked whether every finite von Neumann algebra embeds 

in an ultraproduct of hyperfinite II 1 factors. Initially, this 

grabbed the attention of many operator algebraists; the 

most striking results in this area are due to E. Kirchberg 

who proved many equivalent C*-algebra type statements. 

The question has since attracted mathematicians from 

many areas, including random matrix theory, real algebraic 

geometry, representation theory, free probability, set theory, 

logic, group theory, and of course, operator algebras, but is 

still open. Many results have been obtained in the last five 

years in very diverse areas, so a few people – including the 

organizers – thought that it would be useful and timely to 

bring together people interested in the embedding problem. 

They belong to different mathematical communities and so 

seldom interact with each other. 

The main purpose of the workshop was to learn about each 

others’ attacks on the CEP, and the results and techniques 

involved. Our belief that it is arguably one of the deepest 

problems in operator algebras led us to think that a 

workshop would be ideal to provide an introduction to this 

question both for graduate students and for researchers in 

related areas; this was the second purpose of the workshop. 

The workshop began with two preliminary courses (Thierry 

Giordano on fundamentals of operator algebras and 

Vladimir Pestov on ultrafilters), and an introduction by 

Nate Brown to the problem and his well known equivalent 

operator algebraic reformulations, and his related recent 

results. A subsequent series of lectures was given by Gabor 

Elek on his recent results concerning the relationship 

of CEP with geometric group theory, and in particular, 

soficity. Ilijas Farah, a set theorist interested in operator 

algebras, explained why logicians think it unlikely that CEP 

is independent of ZFC. We then heard from Wing Suet Li, 

Ken Dykema, and Hari Bercovici, discussing recent results 

in the direction of the infinite dimensional Horn problem 

and their relationship with the embedding problem. Finally, 

Markus Schweighofer and Igor Klep explained purely algebraic 

reformulations of the problem from the point of view 

86 

of real algebraic geometry. There was also a problem session 

chaired by Vladimir Pestov. 

The workshop was lively and well attended. We had approximately 

40 participants – including ten graduate students 

– and postdoctoral fellows and participants coming from 

the west coast, the US, South America, Africa, and five 

from Europe. It also attracted researchers from neighbouring 

Ontario universities. 

Not surprisingly, the conjecture was not solved during the 

workshop. However, it was very useful for attendees to learn 

from experts concerning earlier attempts and techniques, 

and partial results obtained en route. We believe that 

the workshop will turn out to be the starting point for 

cross-disciplinary investigations that will lead to new and 

promising results around the Connes embedding problem. 

The workshop also provided useful training for graduate 

students at the beginning of their careers who might now 

decide to work on CEP and who will likely make a meaningful 

contribution. 


Thierry Giordano (Ottawa) 

Introduction to von Neumann algebras 

Vladimir Pestov (Ottawa) 

Ultrafilters and ultraproducts for beginners 


Connes’ Embedding Problem: An Introduction 

Metric spaces associated with embeddable factors 

Gabor Elek (Alfred Renyi Institute of Mathematics ) 

Talk 1: Sofic groups and Connes’ Embedding Problem 

Talk 2: Constant time algorithms and measurable equivalence 

relations. 

Ilijas Farah (York) 

Incompleteness, independence, and absoluteness or: When to 

call a set theorist? 

Wing Suet Li (Georgia Institute of Technology) 

Eigenvalue inequalities, in an embeddable factor and in other 

settings 

Ken Dykema(Texas A&M) 

A linearization of Connes’ embedding problem 

Hari Bercovici (Indiana) 

Schubert calculus for the practical person 

Markus Schweighofer (Université de Rennes) 

A purely algebraic formulation of Connes’ embedding 

conjecture

Igor Klep (Ljubljana) 

Sums of hermitian squares and the BMV conjecture 

Benoit Collins 

CRM-Fields-MITACS Workshop on Lie Groups, 

Group Transforms and Image Processing 

May 16, 2008 

Organizers: Frédéric Lesage (École Polytechnique de Montréal), 

Jiri Patera (Montreal), Hongmei Zhu (York) 

This one-day workshop attracted a spectrum of participants 

from graduate students, post-docs, to young and 

senior faculty in various fields, providing a friendly and 

stimulating environment for exchanging the latest findings 

and fostering collaboration between researchers from different 

academic institutions. 

Featured at the workshop were one 2½-hour mini-course 

and five 1-hour lectures, which summarized the recent 

development of group transforms based on the orbit functions 

of compact Lie groups. 

The workshop began with an intensive mini-course given 

by Jiri Patera, a founder of this research. Jiri introduced us 

to three new families of class functions defined on the maximal 

torus of a compact simply connected Lie group. Each 

class of these functions offers a variety of group transforms 

similar to Fourier and cosine transforms. Group transforms 

using these functions as bases lead to the discrete analogues 

of these transforms, called “discrete orbit-function transforms.” 

Jiri also provided us a recipe on how to compute 

these transforms. Note that the key application of the 

discrete transforms is that their continuous extensions 

smoothly interpolate digital data in any dimension and for 

any lattice with symmetry afforded by the structure of the 

given compact Lie group. 

Afternoon lecture series covered a wide range of research 

from theoretical, computational to application aspects of 

the discrete forms of these transforms. A focal point of 

these talks was the use of these transforms in digital image 

processing. Its power was demonstrated through examples 

in image interpolation, segmentation, edge detection, texture 

identification and image compression. 

The workshop was supported financially by the Centre de 

Recherches Mathématiques, the Mathematics of Information 

Technology and Complex Systems and the Fields 

Institute. 


Abstracts of these talks are available on the Fields webpage: 

www.fields.utoronto.ca/programs/scientific/07-08/ 

liegroups/abstracts.html 

Speakers:(as listed on program itinerary) 

Jirí Hrivnák (Montréal) 

(Anti)symmetric multivariate exponential functions and corresponding 

Fourier transforms 

Frederic Lesage (École Polytechnique de Montréal) 

Compressed sensing in photo-acoustic tomography, a potential 

application for Lie Algebra bases 

Maryna Nesterenko (Montréal) 

Computing with almost periodic functions 

Jiri Patera (Montréal) 

Discrete and continuous multidimensional transforms based 

on C-, S-, and E-functions of a compact semisinple Lie group 

Matthieu Voorons (Montréal) 

Interpolation based on Lie group theory and comparison with 

standard techniques 

Hongmei Zhu (York) 

Integer Lie group transforms 

Hongmei Zhu 

Eighth Algorithmic Number Theory Symposium 

ANTS-VIII 


Held at the Banff Centre, Banff, Alberta 

Organizers: Mark Bauer (Calgary), Josh Holden (Rose-Hulman 

Institute), Mike Jacobson (Calgary), Renate Scheidler 

(Calgary), Jon Sorenson (Butler University) 

Since their inception in 1994, the bi-annual ANTS meetings 

have become the premier international forum for the presentation 

of new research in computational number theory. 

They are devoted to algorithmic aspects of number theory, 

including elementary number theory, algebraic number 

theory, analytic number theory, geometry of numbers, 

algebraic geometry, lattices, finite fields, and cryptography. 

This was the first time ANTS was held in Canada; previous 

ANTS meetings have taken place in North America, 

Europe, and Australia. With 138 participants from 18 countries 

spanning all six populated continents, ANTS-VIII was 

a truly international event. Attendees included researchers 

from academia, industry and government as well as a considerable 

number of students and postdoctoral fellows. 

87


88 

anTS-Viii participants 

As always, the meeting was accompanied by a proceedings 

volume. The ANTS-VIII Proceedings have appeared as 

volume 5011 of Springer’s Lecture Notes in Computer Science 

series. Twenty-eight articles and two invited papers were 

accepted for publication. Topics range from computations 

and cryptography on algebraic curves to the construction 

of algebraic surfaces, function fields, modular forms, and 

integer factorization. In keeping with the high standard of 

the ANTS proceedings, each submitted paper was carefully 

reviewed by at least two experts external to the ANTS-VIII 

Program Committee. 

Four plenary lectures represented the highlight of the scientific 

activities at the meeting. Johannes Buchmann spoke on 

lattice-based signatures in cryptography. Andrew Granville 

lectured on running time predictions for square products, 

which play a central role in integer factoring algorithms. 

François Morain provided a survey on algorithms for computing 

isogenies on low genus curves. The celebrated Pell 

equation was the subject of Hugh Williams’ presentation, 

who has recently completed a book on this subject. 

In addition to the plenary lectures, the scientific program 

included talks by all the authors, or author teams, whose 

papers appeared in the proceedings. 14 research posters 

were also on display for the duration of the conference. All 

the talks as well as the posters and their abstracts are available 

at the conference website www.ants.math.ucalgary. 

ca. Other conference activities included an opening reception 

(sponsored by Microsoft Research), a banquet, and a 

free afternoon which many attendees spent sight-seeing or 

hiking in the scenic Canadian Rockies. 

As in previous years, the Selfridge Prize in Computational 

Number Theory, sponsored by the Number Theory Foundation, 

was awarded to the authors of the best conference 

paper, as selected by the ANTS Program Committee. This 

year’s prize went to Computing Hilbert Class Polynomials 

by Juliana Belding (Maryland), Reinier Bröker (Microsoft 

Research), Andreas Enge (École Polytechnique) and Kristin 

Lauter (Microsoft Research). In addition, for the first time 

at ANTS, there was a best poster award which was determined 

by a vote of all the ANTS participants. The winner 

was the poster Genus 2 Curves With Split Jacobians by Kevin 

Doerksen (SFU). 

Plenary Speakers: (in alphabetical order) 

Johannes Buchmann (TU Darmstadt) 

Andrew Granville (Montreal) 

Francois Morain (Ecole Polytechnique, Paris) 

Hugh Williams (Calgary) 

Renate Schiedler 

Fifth International Workshop on Taylor Model Methods 


Organizers: Ken Jackson (Toronto), Martin Berz (Michigan 

State) 

The previous four meetings in this series were all held in 

Florida a week or two before Christmas, so this was a hard 

act to follow. However, the Fields workshop was eminently 

successful: the weather was good, the excursion to Niagara 

Falls was memorable, the Fields facilities were great and the 

talks were excellent.

The focus of the meeting was the use of Taylor Models 

(i.e., essentially Taylor Series with rigorous error bounds) 

to compute approximate solutions with guaranteed error 

bounds for problems associated with ODEs, PDEs, solar 

system dynamics, dynamical systems, global optimization 

and constraint satisfaction. One of the emerging trends 

in this area, discussed at this meeting, is the use of Taylor 

Model Methods to prove results associated with dynamical 

systems. Sheldon Newhouse gave an excellent introduction 

to this area and Johannes Grote and Alexander Wittig gave 

overviews of their PhD research in this topic. 

One of the great advantages of holding a small workshop at 

the Fields Institute is flexibility. For example, two speakers 

were not able to come to Toronto and so, through the 

computer wizardry of Alexander Wittig and the excellent 

audio-visual facilities and the accommodating support staff 

at the Fields, we were treated to a live two-way video presentation 

of their talks. Moreover, the talk Complexity-theoretic 

barriers to validated solution of initial value problems by Akitoshi 

Kawamura inspired John Pryce to volunteer to give 

an additional talk On the Ilie-Corless polynomial complexity 

proof, which was added at the last minute as the final talk of 

the meeting. 

The slides and audio recordings of all the talks are online at 

www.fields.utoronto.ca/audio/07-08/#taylor-model. 

In addition, we are preparing proceedings for the workshop 

that will be published in the Fields Institute’s Communications 

Series. 

Taylor Model Methods workshop participants 



Martin Berz (Michigan State) 

Taylor Model Methods – Introduction and Overview 

Sheldon Newhouse (Michigan State) 

Numerical and Rigorous Aspects of Low Dimensional 

Dynamical Systems 

Johannes Grote (Michigan State) 

Rigorous Classification of Manifold Tangles and Bounds for 

Entropy 

Yosef Yomdin (Weizmann) 

Some High-Order Taylor-Model Based Methods for Solving 

PDEs 

Gianni Arioli (Milan) 

A Functional Analysis Approach to Computer Assisted Proofs 

based on Taylor Expansions 

Roberto Armellin (Milan) 

Rigorous Global Optimization of Impulsive Planet to Planet 

Transfers 

John Pryce (Cranfield) 

DAETS: A Differential-Algebraic Equation Code in C++ for 

High Index and High Accuracy 

Pierluigi DiLizia (Milan) 

High Order Integration and Sensitivity Analysis of Differential 

Algebraic Equations using Differential Algebra 

Pierluigi DiLizia (Milan) 

Station Keeping around Halo Orbits using Differential Algebra 

Martin Berz (Michigan State) 

New Algorithms for Efficient Taylor Model Operations 

Including Arbitrary Precision 

Youn-Kyung Kim (Michigan State) 

A High Order Method for Computations of Rigorous Lower 

Bounds of Smooth Functions near Local Minimizers 

Nathalie Revol (École normales upieure de Lyon) 

Automatic Adaptation of the Computing Precision 

Markus Neher (Karlsruhe) 

On the Blunting Method in Verified Integration of ODEs 

Kyoko Makino (Michigan State) 

Recent Advances in the Rigorous Integration of Flows of ODEs 

with Taylor Models 

Alexander Wittig (Michigan State) 

Computer Assisted Proof of High Period Fixed Points in the 

Henon Map 

89


Roland Zumkeller (Microsoft Research/INRIA) 

Machine Checkable Correctness Proofs 

Akitoshi Kawamura (Toronto) 

Complexity Theoretic Barriers to Validated Solutions of Initial 

Value Problems 

Abedallah Rababah (Jordan University of Science and 

Technology) 

Hermite Approximation with High Accuracy for Space Curves 

in R d 

John Pryce (Cranfield) 

On the Ilie-Corless Polynomial Complexity Proof 

Ken Jackson 

36th Canadian Annual Symposium on Operator Algebras 

and Their Applications (COSy) 


Organizers: Man-Duen Choi (Toronto), George A. Elliott 

(Toronto), Raphael Ponge (Toronto), Andrew S. Toms 

(York) 

The focus of the meeting returned to the original: algebras 

of operators on Hilbert space. The style of the meeting has 

achieved a steady state over the years, which was maintained 

this year as well. There were eleven plenary speakers 

(50 minutes each) and twenty-nine other talks of 30 

minutes. The only scheduling difference between this meeting 

and its predecessors was our willingness to have a few 

slightly longer days in order to avoid parallel sessions. It was 

felt this would give the best possible exposure to younger 

researchers. 

The funds from Fields and the NSF together with the 

registration fees were used to support the plenary speakers, 

graduate students and postdoctoral fellows. In the end, no 

graduate students or postdoctoral fellows paid registration 

fees and all those who registered in time were reimbursed 

for their travel expenses. 

The plenary speakers were Bruce Blackadar (Reno), Berndt 

Brenken (Calgary), Nate Brown (Penn State), Marius Dadarlat 

(Purdue), Ken Davidson (Waterloo), Magnus Landstad 

(NTNU), Jamie Mingo (Queen’s), Chris Phillips (Oregon), 

Roland Speicher (Queen’s), John Phillips (Victoria), Dana 

Williams (Dartmouth). The topics covered in their lectures 

included non-stable K-theory, free probability theory, noncommutative 

geometry, crossed product C*-algebras, and 

the Cuntz subgroup. 

90 

More than 70 participants registered for the conference, 

and many more graduate students from the Toronto area 

took part in all or part of the meeting. This level of attendance 

compares favourably with previous COSys, where 

attendance has averaged 40-60. We feel the location (both 

Fields and Toronto) played an important role in attracting 

participants. 

The scientific value of the meeting was high, going well 

beyond the dissemination of new results. Several participants 

were able to make progress on joint projects 

during the week, the organizers included! The meeting 

also afforded students the opportunity make contacts and 

discover postdoctoral opportunities for the future. The 36 th 

annual COSy was an unqualified success, and we hope that 

Fields will consent to host our meeting in years to come. 

Plenary Speakers: (as listed on program itinerary) 

Marius Dadarlat (Purdue) 

One-parameter continuous fields of AF-algebras 

Man-Duen Choi (Toronto) 

Non-commutative magic 

Asger Tornquist (Toronto) 

An anti-classification Theorem for von Neumann factors 


The Cuntz Semigroup 

Doug Farenick (Regina) 

Injective envelopes of continuous trace C*-algebras 

Andrew Toms (York) 

Hilbert modules over C*-dynamical systems 

Leonel Robert (Toronto) 

The cones of lower semicontinuous traces and quasitraces of a 

C*-algebra 

Matthew Kennedy (Waterloo) 

Invariant subspaces of non-associative algebras of compact 

operators 

Bruce Blackadar (Reno) 

Ideal structure of NF algebras and the UCT revisited 

Jonathan Novak (Queen’s) 

Some properties of truncated Haar unitary random matrices 

Remus Floricel (Regina) 

The asymptotic flow of an E0-semigroup 

Jamie Mingo (Queen’s) 

Correlations of Eigenvalues of Random Matrices


Nonseparable UHF algebras 

Stefanos Orfanos (Purdue) 

Properties of Generalized Bunce-Deddens algebras 

Mitja Mastnak (Waterloo) 

Realizing irreducible semigroups and real algebras of compact 

operators 

Alin Ciuperca (Toronto) 

Equivalence between two invariants for C*-algebras 

Ileana Ionescu (Philadelphia) 

C-Orbit reflexivity of Hilbert Space Operators 

Chris Phillips (Eugene) 

Connected MASAs in UHF algebras 

Volker Runde (Alberta) 

Uniform continuity over locally compact quantum groups 

John Phillips (Victoria) 

An index theory for certain Gauge Invariant KMS States on 

C*- Algebras 

Dan Kucerovsky (UNB) 

Z-stability, purely infinite corona, and skeletons 

Roland Speicher (Queen’s) 

Resolvents and distances between operators 

Heydar Radjavi (Waterloo) 

On local-to-global properties of semigroups of operators 

Magnus Landstad (NTNU, Trondheim, Norway) 

The Hecke algebra of Bost-Connes revisited 

George Elliott (Toronto) 


Dana Williams (Dartmouth) 

Proper actions on $C^*$-algebras 

Ping Wong Ng (Louisiana) 

Nuclearity and weak uniqueness 

Wend Werner (Westfälische Wilhelms-Universität) 

On a class of Hilbert C*-manifolds 

Bamdad Yahaghi (IPM, Tehran) 

A short survey of Burnside type theorems 

Ahmed Al-Rawashdeh (Jordan University of Science and 

Technology) 

Unitary groups as a complete invariant 

Ken Davidson (Waterloo) 

Topological stable rank of Banach algebras 

Claus Koestler (UIUC) 

Braidability 


Martin Mathieu (Queen’s University Belfast) 

The Maximal C*-Algebra of quotients as an operator bimodule 

David Kribs (Guelph) 

Complementarity in quantum cryptography and error correction 

Berndt Brenken (Calgary) 

A dynamical core for topological quivers 

Julien Giol (Texas A&M University) 


Dilian Yang (Waterloo) 

Representations of higher rank graph algebras 

Hun Hee Lee (Waterloo) 

Projectivity of L p (VN(G)) as a left A(G)-module 

Emily Redelmeier (Queen’s) 


Andrew Toms 

Symposium on Dependent Data Structures 



Organizers: Patrick Farrell, Shirley Mills, Chul Park, and 

Sanjoy Sinha (Carleton) 

The goal of this symposium was to provide a platform to 

discuss recent developments for modeling dependent data 

structures. The workshop attracted over 60 participants 

from Canada and abroad, and began with opening remarks 

by J.N.K. Rao giving a brief overview of dependent data 

analysis and its applications in various areas of survey sampling 

and clinical trials. 

The scientific program was both diverse and intense, consisting 

of eighteen talks including three keynote speeches, 

six invited and nine contributed talks. Most of the talks 

focused on both theoretical and practical aspects of modeling 

and statistical analyses of dependent data which include 

survey data, longitudinal and clustered data, and genetic 

data. Along with various types of modeling techniques for 

correlated data, linear mixed models and generalized linear 

mixed models were extensively discussed in many of the 

talks. 

David Brillinger gave a keynote speech on the first day of 

the symposium in which he discussed the analysis of data 

91


from a biological experiment on the muscle spindle. The 

experiment involved two input and two output neurons, 

and the analysis combined the results of a time domain 

approach with those of a frequency domain approach to 

obtain new information about the behaviour of the muscle. 

Charles McCulloch gave his keynote speech on the second 

day and discussed prediction of random effects in both 

linear and generalized linear mixed models. He studied 

the consequences of an incorrect specification of the distribution 

of random effects and investigated the impact of 

misspecification with a focus on prediction of the realized 

values of the random effects. 

On the third day in his keynote speech, Richard Cook 

discussed survival data in the case of dependent censoring 

with recurrent events. He described a bivariate mixed Poisson 

model which was used to investigate the consequences 

of an event-dependent censoring scheme arising in many 

clinical trials in which subjects are withdrawn from a study 

when they experience a specified number of the more 

severe events. 

Along with many other interesting talks, there were also 

stimulating discussions by the invited speakers Subhash Lele 

on data cloning for simplified likelihood inference in mixed 

models, J.N.K. Rao on bootstrap methods for analyzing 

complex survey data, and Brajendra Sutradhar on generalized 

quasi-likelihood inference for longitudinal data. 

The symposium was funded by the Fields Institute, 

Carleton University, and the School of Mathematics and 

Statistics at Carleton University. 


Ehsanes Saleh (Carleton) 

Dependent data and genomics 

Subhash Lele (Alberta) 

Data cloning: a simple approach for computing maximum 

likelihood estimates for mixed models 

David Sankoff (Ottawa) 

The generalized adjacency criterion in comparative genomics 

Jason Nielsen (Carleton) 

Clustered and time series data 

Leilei Zeng (SFU) 

Methods for clustered/correlated failure time data 

Vickneswary Tagore & Brajendra Sutradhar (Memorial) 

Conditional inference in linear versus non-linear models for 

binary time series 

92 

J.N.K. Rao (Carleton) 

Time series with applications to biology 

David Brillinger (Berkeley) 

Assessing connections in networks with point process input 

and output with a biological example 

Chul Park (Carleton) 

Categorical data 

Vinzenz Erhardt (speaker) & Claudia Czado (Munich) 

Generalized estimating equations for generalized Poisson 

count data with regression effects on the mean and dispersion 

level applied to patent outsourcing rates 

Salehin Chowdhury (Carleton) 

Association analysis of disease status with a candidate gene 

using generalized linear mixed models 

Karelyn Davis (speaker), Chul G. Park, and Sanjoy K. Sinha 

(Carleton) 

Inequality constraints in generalized linear and mixed models 

with missing data 

Charmaine Dean (SFU) 

Mixed model 1 

Charles McCulloch (San Francisco) 

Prediction of random effects and effects of misspecifying their 

distribution 


Mixed model 2 

Brajendra Sutradhar (Memorial) 

GQL inferences in stationary versus non-stationary GLLMs 

Michel Chavance & Sylvie Escolano (INSERM, France) 

Misspecifying random effects in generalized linear mixed 

effects models 

Mohamedou Ould-Haye (Carleton) 

Correlated data – applications to survey and clinical data 

Geoff Rowe (Statistics Canada) 

Child birth, labour market transitions, and residential mobility: 

use of correlatedevent data to introduce heterogeneity in the 

LifePaths microsimulation model 

Hyang Mi Kim (Calgary) 

Bias in the estimation of exposure effects with endividual – 

or group-based exposure assessment 

Sanjoy Sinha (Carleton) 

Statistical genetics 

JC Loredo-Osti (Memorial) 

Pedigree complexity and genetic inference via likelihood

Arafat Tayeb (Centre de Recherche UL) 

Latent class model under familial dependence with missing 

data 

Brajendra Sutradhar (Memorial) 

Correlated survival data 


A copula random effect model for multi-type recurrent events 

under event-dependent censoring 

Charles McCulloch (San Francisco) 

Mixture model and survey data 

J.N.K. Rao (Carleton) 

Bootstrap methods for analyzing complex sample survey data 

with dependent structures 

Charmaine Dean (SFU) 

Spatio-temporal and mixture models for multi-state processes 

Bruce Richter 

Ontario Combinatorics Workshop 


Held at the University of Waterloo 

Organizers: Chris Godsil and Bruce Richter (Waterloo) and 

Daniel Panario and Brett Stevens (Carleton) 

This workshop provides an opportunity for graduate 

students in combinatorics in different institutions to present 

their work in a very supportive environment. A main 

point of the workshop is to introduce graduate students 

from different schools to each other. This provides them an 

opportunity to share their interests in a way that is just not 

possible in a traditional meeting. The noise level at the coffee 

breaks was music to our ears! 

This year’s OCW had 45 participants, including 15 women, 

from as far away as Memorial University of Newfoundland, 

with most of the participants coming from Ottawa, Toronto 

and Waterloo. Altogether 10 different universities were 

represented. 

The 18 graduate student talks covered a diverse selection of 

topics, including graph and hypergraph colouring, strongly 

regular graphs, decomposing graphs and hypergraphs into 

circuits, design theory, hyperplane arrangements, applications 

of Markov chains in graph colouring algorithms, 

computational complexity and approximation algorithms. 

The faculty in attendance all commented on the high quality 

of the presentations, which made for a very enjoyable 

and instructive conference. 


At each OCW, the Peter Rodney Memorial Book Prize is 

presented to the student judged to have given the best talk. 

This award honours the memory of Peter Rodney, who 

obtained his Ph.D. from University of Toronto in 1993 and 

died an untimely death aged 30 in 1995. Donations may be 

made to the fund care of the Department of Mathematics at 

the University of Toronto. 

This year’s winner of the book prize is Jessica McDonald 

from the University of Waterloo for her talk Achieving 

maximum chromatic index in multigraphs. 


Penny Haxell (Waterloo) 

Independent transversals 

Jessica McDonald (Waterloo) 

Achieving maximum chromatic index in multigraphs 

Natalie Mullin (Waterloo) 

Constructing strongly regular graphs 

Robert Bailey (Carleton) 

Hamiltonian decompositions of complete k-uniform hypergraphs 

Daniela Silvesan (Memorial) 

The intersection spectrum of Skolem sequences 

Bill Martin (Worcester Polytechnic Institute) 

The story of (T,M,S)-nets 

Martin Pei (Waterloo) 

List colouring Steiner triple systems 

Shonda Gosselin (Ottawa) 

Self-complementary uniform hypergraphs 

Andrea Burgess (Ottawa) 

Closed trail decompositions of complete equipartite graphs 

Amy Cameron (Ottawa) 

A simpler 3/2-approximation algorithm for the multi-twoedge 

connected subgraph problem 

Matei David (Toronto) 

Separating number-on-forehead communication complexity 

classes RP and NP 

Feng Xie (McMaster) 

Hyperplane arrangements with large average diameter 

Prosenjit Bose (Carleton) 

An overview of geometric spanners 

Christina Boucher (Waterloo) 

Towards identifying when a consensus exists: a study of 

probablistic algorithms for Consensus Sequence 

93


Jonathan Novak (Queen’s) 

Some combinatorial properties of truncated random unitary 

matrices 

Brendan Lucier (Toronto) 

Fast Mixing for 3-colourings on bounded-degree trees 

Bruce Richter 

Noncommutative Geometry Workshop 


Organizers: Masoud Khalkhali (Western), Matilde Marcolli 

(Max Planck Institute, Bonn), and Guoliang Yu (Vanderbilt) 

This was the second international conference on Noncommutative 

Geometry (NCG) at the Fields Institute – the first 

took place 13 years ago in June 1995 at the Fields Institute’s 

temporary site in Waterloo. The proceedings of that meeting 

were published and are a testament to the breadth and 

scope of the subject at that point. Several of the speakers in 

this meeting also spoke at the 1995 meeting, but one could 

not fail to notice a much younger generation of mathematicians 

in attendance this year. 

A highlight of the meeting was the Distinguished Lecture 

Series by Alain Connes that took place during this meeting. 

Connes gave three lectures with titles: The spectral characterization 

of manifolds, A CKM invariant in Riemannian 

geometry, About the field with one element. In his introduction 

to Connes’ lectures, Juris Steprāns, the deputy director 

of the Fields, mentioned that Connes is the first mathematician 

who has delivered a Distinguished Lecture series for a 

second time. In fact his first lecture series also took place at 

the previous meeting in 1995. Since there will be a separate 

review and report of Connes’ lectures, in the following we 

shall merely report on the conference talks. 

All areas of noncommutative geometry were present in 

the talks. Roughly speaking one can divide the talks into 

3 groups. This is not an artificial division, since in fact 

it coincides with the three phases of the development of 

Noncommutative Geometry by Alain Connes and his 

school. The first group of talks touched on aspects of 

noncommutative geometry related to index theory and its 

generalizations, the Baum-Connes conjecture and applications 

to algebraic topology (the Novikov conjecture), and 

the relevant tools like cyclic cohomology, K-theory and 

KK-theory. The second group was related to metric aspects 

of noncommutative geometry, spectral triples, applications 

94 

to the standard model of elementary particles and quantum 

field theory. Finally there were several talks that highlighted 

recent interactions between number theory, algebraic 

geometry and Noncommutative Geometry. 

The talks by Higson, Guentner, Baum, Emmerson, Nica 

and Pourkia covered aspects of NCG related to the Baum- 

Connes conjecture, KK-theory and cyclic cohomology, and 

its applications to noncommutative geometry. Those by 

Tang, Fathizadeh, Phillips, Tsygan and Gorokhovsky were 

related to index theory in the noncommutative setting. 

Talks by Landi, Rieffel, Li, Ponge, Hajac, and Wulkenharr 

centered around the notion of spectral triples, Dirac operators 

on noncommutative spaces and quantum groups. 

Finally the talks by Consani, Ha, Mahanta, Plazas, and Yao, 

dealt with interactions between noncommutative geometry, 

number theory, algebraic geometry, and the theory of 

motives. 


Nigel Higson (Penn State) 

Mackey’s analogy and admissible representations of complex 

semisimple groups 

Jorge Plazas (IHES) 

Heisenberg modules and arithmetic properties of noncommutative 

tori 

Yi-Jun Yao (Vanderbilt) 

Some results on Rankin-Cohen deformations 

Marc Rieffel (Berkeley) 

Dirac operators for coadjoint orbits 

Xiang Tang (Washington) 

Algebraic higher index theorems 

Arash Pourkia (Western) 

Hopf-cyclic cohomology in braided monoidal categories 

Giovanni Landi (Trieste) 

Monopoles and Laplacians on quantum Hopf bundles 

Alexander Gorokhovsky (Colorado) 

Algebraic index theorem for Fourier integral operators 

Bogdan Nica (Vanderbilt) 

Relatively spectral morphisms and applications to K-theory 

Raphaël Ponge (Toronto) 

Noncommutative geometry and lower dimensional volumes in 

Riemannian geometry 

Erik Guentner (Hawaii at Manoa) 

Decomposition complexity of metric spaces

John Phillips (Victoria) 

An index theory for certain gauge invariant KMS states on 

C*-algebras 

Farzad Fathizadeh (Western) 

Towards a local index formula for twisted spectral triples 

Boris Tsyganf (Northwestern) 

Deformation quantization of Lagrangian submanifolds 

Raimar Wulkenhaar (Münster) 

A spectral triple for harmonic oscillator Moyal space 

Piotr M. Hajac (Polish Academy of Sciences) 

Equivariant pullbacks and finite free distributive lattices 

Eugene Ha (Johns Hopkins) 

On Z structures and the Bost-Connes system 

Paul Baum (Penn State) 

Geometric structure in the representation theory of reductive 

p-adic groups 

Katia Consani (Johns Hopkins) 

The integral BC-endomotive and its reduction mod p 

Heath Emerson (Victoria) 

Duality in equivariant Kasparov theory 

Snigdhayan Mahanta (Toronto) 

Noncommutative correspondence categories and homotopy 

groups of separable C*-algebras 

Hanfeng Li (SUNY Buffalo) 

Metric aspects of noncommutative Heisenberg manifolds. 

Masoud Khalkhali 

Conference on Hyperbolic Problems: Theory, Numerics 

and Applications (HyP2008) 

June 9–13, 2008 

Held at the University of Maryland 

Organizers: Jian-Guo Liu, Eitan Tadmor and Athanasios 

Tzavaras (University of Maryland) 

This was the 12 th of a very successful series of biennial 

conferences that has become the focal meeting in the area 

of nonlinear hyperbolic systems, and traditionally attracts a 

number of researchers working in all aspects of the subject: 

analysis, modeling, numerical analysis and computation. 

As hyperbolic systems are omnipresent in convection dominated 

and fast-transport processes, the field has expanded 

over the years and reaches out to diverse subjects as can be 

attested by a mere review of the titles and abstracts of the 

talks. 


Beyond the traditional subjects covered in this Series of 

Conferences, Hyp2008 purported to highlight themes that 

have attracted recent attention and are of interest to the 

hyperbolic PDE community. There were: 

• Singular limits – zero-viscosity, relaxation, incompressible 

limit, semi-classical limits; 

• Nonlinear wave patterns in multi-dimensions; 

• Particle/molecular dynamics in e.g., kinetic methods, 

magneto-hydrodynamics etc; 

• Theory and numerics of multiphases and interfaces, 

including boundary layers, phase boundaries and multiphase 

wave propagation; 

• Transport in complex environments: homogenization, 

semi-classical limits, scattering in random media, porous 

media, biological applications, network and traffic flows; 

• Model reduction – coupling and decompositions in 

passage from the microscopic to the macroscopic, in 

numerical issues in transitional regimes, in decomposition 

of fast and slow dynamics, and in coupling of 

Lagrangian-Eulerian descriptions. 

On Wednesday morning there was the session on open 

problems in which some prominent researchers presented 

their views on the direction of the subject and outlined 

open problems that can be addressed in relatively shortterm 

timeframe. Tai-Ping Liu (Stanford) took a long-term 

perspective and talked about the rigorous passage from 

N-particle systems to the Boltzmann equation. Randy 

LeVeque (Washington) thought that opportunities for 

new interdisciplinary collaborations are abundant beyond 

the traditional field of fluid mechanics (around which 

hyperbolic theory developed), and that researchers in 

the hyperbolic community should reach out to fields like 

biology, material science or seismology. Denis Serre (ENS- 

Lyon) emphasized the need for developing methods for 

2-D Riemann problems that give mixed-type systems, and 

offered an account of the status of the stability problem 

for continuous and discrete shock profiles. Francois Golse 

(Ecole Polytechnique) talked about the need to develop 

mathematical theory for boundary-value problems for 

kinetic equations and about extending the relative entropy 

method to Boltzmann equations. Peter Markowich (Cambridge) 

urged developing further connections between 

hyperbolic theory and kinetic or dispersive theories and 

gave as an example the problem of small-dispersion limit 

for nonintegrable dispersive equations. 

In his banquet talk, Constantine Dafermos gave a personable 

account of the life and the brilliant career of Ron 

DiPerna. Ronald J. DiPerna (1947-89) was a mathematician 

95


of exceptional courage and vision whose work permeates 

many aspects of the modern theory of nonlinear hyperbolic 

systems and kinetic theory. At the time of his unfortunately 

premature death he was a Professor of Mathematics at the 

University of California at Berkeley. 

On the conference web-page http://hyp2008.umd.edu/ 

index.htm the reader can find the titles and abstracts of 

the 13 plenary, 15 invited and over 120 contributed talks, 

attended by some 230 participants from 26 countries. 

The support from a number of funding agencies, including 

the NSF, ONR and AFOSR with additional contributions 

from the Fields Institute and the IMA was very helpful 

in financing the participation of young mathematicians, 

women and participants from Eastern Europe and in 

defraying the expenses of the plenary and invited speakers. 

Plenary Speakers: (as listed on program itinerary) 

Sylvie Benzoni-Gavage (Lyon) 

Multi-d Shock Waves and Surface Waves 

Gui-Qiang Chen (Northwestern) 

Shock Reflection-Diffraction and Multidimensional Conservation 

Laws 

Shuxing Chen (Fudan) 

Study on Mach Reflection and Mach Configuration 

Michael Fisher (Maryland) 

Some Fruits of Genius: Lars Onsager and the Ising Model 

Francois Golse (Paris VII) 

Quantitative Compactness Estimates for Conservation Laws 

Shi Jin (Wisconsin-Madison) 

Liouville Equations and Hamiltonian Systems with Discontinuous 

Hamiltonians: Computation of High Frequency 

Waves in Heterogeneous Media 

Alex Kiselev (Wisconsin-Madison) 

Some Recent Results on 2-D Surface Quasi-Geostrophic Equation 

Peter Markowich (Cambridge) 

On Nonlinear Dispersive Equations in Periodic Structures: 

Semiclassical Limits and Numerical Schemes 

Sergei Novikov (Maryland) 

On the Hamiltonian 1st-Order PDE Systems 

Stanley Osher (UCLA) 

New Algorithms in Information Science and Connections with 

Time-Dependent PDEs 

96 

Benoit Perthame (Paris VI) 

Hyperbolic and Kinetic Model for Cell Motion 

Benedetto Piccoli (Istituto per le Applicazioni del Calcolo 

“Mauro Picone”, Rome) 

Traffic Flow on Networks: Conservation Laws Models 

Saul Teukolsky (Cornell) 

Simulations of Black Holes and Gravitational Waves 

Thanos Tzavaras and Eitan Tadmor 

Conference on Formal Power Series and Algebraic 

Combinatorics (FPSAC) 


Held in Valparaiso, Vina del Mar, Chile 

Organizers: Federico Ardila (San Francisco State), Hélène 

Barcelo (Arizona State), María Ines Icaza (Universidad 

de Talca), Christian Krattenthaler (Wien, Co-chair) Luc 

Lapointe (Universidad de Talca, Chair), Jennifer Morse 

(Drexel) 

The purpose of this annual conference is to deepen the 

relations between combinatorics and other fields of 

mathematics and sciences. In particular, the topics include 

combinatorics and the relations with other parts of mathematics, 

physics, computer science, and biology. Because of 

its success, it has developed into one of the most important 

conferences in this field. The series of conferences started 

in 1988 in Lille, France, with 30 participants, concentrating 

on formal languages. A large group of closely affiliated 

combinatorialists in Paris, Bordeaux and Montréal then 

widened its scope. The 4th FPSAC/SFCA, held in Montréal 

in 1992, was the first to be held outside of France. Since 

then, the location of the conference changes country every 

year. This brings a lot of stimulating exchanges and tightens 

international bonds. Moreover, the participation of promising 

junior researchers and graduate students is especially 

encouraged. A good proportion of the invited speakers are 

mathematically young, and graduate students and postdocs 

are supported financially. 

There were 120 participants this year, more then 75% of 

them young researchers or graduate students. Valentin 

Feray (France) was awarded the US$500 Elsevier prize 

for the best extended abstract by a student. There were 10 

Invited lectures, 27 contributed presentations, a 40-poster 

session, and software demonstrations, all this without parallel 

sessions. The poster session was as usual very exciting 

and popular, with lots of exchange and discussion.

More information and conference slides can be found at 

inst-mat.utalca.cl/fpsac2008/ 


Marcelo Aguíar (Texas A&M) 

A unified approach to Hopf algebras 

Michael Albert (University of Otago, New Zealand) 

Growth rates of pattern classes 

Jonathan Brundan (Oregon) 

Highest weight categories arising from Khovanov´s diagram 

algebra 

Dmitry Feichtner-Kozlov (Universität Bremen, Germany) 

Combinatorial algebraic topology 

Ian Grojnowski (Cambridge) 

Title not available 

Gilbert Labelle (UQAM) 

Mes aventures mathématiques avec Pierre Leroux 

Alexander Postnikov (MIT, USA) 

Title not available 

María Ronco (Universidad de Valparaiso, Chile) 

Bialgebras in the category of S modules 

Carla Savage (North Carolina) 

Euler´s partition theorem and the combinatorics of l-sequences 

Francois Descouens 

Fields Workshop on New Directions in Cryptography 



Organizers: Ian Blake (Toronto), Ali Miri and Monica 

Nevins (Ottawa) 

This hugely successful event drew over 90 participants and 

speakers from all over North America, and from as far away 

as England, Australia and Jordan. 

The first day of the workshop was devoted to mini-courses 

on some of the major themes in modern cryptography. In 

the morning, Kenny Paterson gave a wonderful overview 

of the history and necessity of Identity-Based Encryption, 

and then brought the audience to the current cutting edge 

of research in that area. The afternoon’s course, given by 

Ali Miri, gave an overview of the techniques and ideas of 

accelerating scalar multiplication on Elliptic Curve Cryptosystems 

(ECC), with particular emphasis on recent open 

problems. 


The second day featured invited lectures by worldrenowned 

researchers working in Canadian universities, 

in mathematics, computer science and engineering. Many 

of the speakers specifically highlighted current open problems, 

both theoretical and practical in nature, for graduate 

students to explore. The opening talk by Kumar Murty 

explored the mysteries of hash functions. New variants of 

elliptic curves for use in cryptography were the subject of 

Renate Scheidler’s talk, while Francesco Sica explored new 

ideas in scalar multiplication on algebraic curves. Doug 

Stinson focused on new results on authentication protocols, 

and Amr Youssef presented analysis of Boolean functions 

for use in cryptography. Evangelos Kranakis closed the 

day with an intriguing and thought-provoking talk about 

security models. 

The final day of the workshop featured speakers from 

government and industry. The first talk, by representatives 

of the CSEC, gave an overview of the mandate and interests 

of this governmental body and was of particular interest to 

the many graduate students in attendance. The final three 

talks, by Rene Struik, Tom St Denis and Dana Neustader 

and Phil Eisen, introduced a variety of problems and issues 

that are subjects of intense industrial research. These range 

from speeding up implementations of ECC to ensuring 

security in a world where even cryptographic icon “Bob” 

can’t be trusted. 

Cloakware and Certicom generously offered additional 

sponsorship for this workshop. Consequently, all students 

and junior researchers who applied for funding received 

some support for their travel and accommodation expenses. 

Moreover, the workshop was able to provide all coffee 

breaks, as well as lunches on the three days, at no charge to 

the participants. These breaks and meal times invited and 

encouraged much additional interaction among the participants 

and speakers, and were enjoyed by all. 

The talks were held in the beautiful SITE building of the 

University of Ottawa, which overlooks the Rideau Canal. 

After delightful sunny weather the first two days, some rain 

arrived on the last day. Nevertheless, some participants 

braved the soggy weather to enjoy the boat cruise on the 

Rideau Canal after the close of the workshop. Three intense 

days and a wealth of problems to pursue: we look forward 

to the next time! 


Kenny Paterson (London) 

Recent advances in identity-based encryption 

97


Ali Miri (Ottawa) 

Accelerating scalar multiplication of elliptic curve crypto sytems 

Phil Eisen (Cloakware) 

It’s Not the Size of Your Key That Matters, It’s How You Use It 

Evangelos Kranakis (Carleton) 

Security Models: Prospects, Perspectives, Directions 

Kumar Murty (Toronto) 

Recent developments in Hash functions 

Renate Scheidler (Calgary) 

Real Hyperelliptic Curves 

Francesco Sica (Mount Allison) 

Complex Double Bases applied to Scalar Multiplication on 

Algebraic Curves 

Doug Stinson (Waterloo) 

Recent Results on the Design and Analysis of Manual Authentication 

Protocols 

Amr M. Youssef (Concordia) 

On Cryptographic Properties of Boolean Functions 

Rene Struik (Certicom) 

Speed-ups of elliptic curve-based schemes 

Dana Neustadter (Elliptic Semiconductor) 

Elliptic Curves over Prime and Binary Fields in Cryptography 

Monica Nevins 

Summer School in Analytic Number Theory and 

Diophantine Approximation 

June 30–July 11, 2008 


Organizing committee: Nathan Ng (Lethbridge), Damien 

Roy (Ottawa) 

Scientific advisory committee: Nathan Ng, Damien Roy, 

Kannan Soundararajan (Stanford) 

This two week summer school attracted 85 participants 

from 46 different post-secondary institutions all over the 

world. Thanks to financial support from the Fields Institute 

and the National Science Foundation, we were able to 

partially fund the living and travel expenses of 19 Canadian 

students, 15 students from the United States, and 18 

students from 10 other countries. The main objective of the 

school was to give young mathematicians an opportunity to 

learn the latest methods and results in analytic number theory 

and Diophantine approximation. These closely related 

98 

fields have made considerable progress in the last ten years. 

Some examples of important results that have recently been 

proven are Goldston, Pintz, and Yildirim’s theorem on 

small gaps between primes and Ball and Rivoal’s theorem 

on infinitely many irrational odd zeta values. The summer 

school exposed the participants to key ideas and tools in 

these respective fields. Moreover, it was affiliated to the 

tenth conference of the Canadian Number Theory Association 

(CNTA X) which took place July 13–July 18, 2008 in 

Waterloo. 

The first week of the school consisted of introductory 

lectures by Michel Waldschmidt (Paris VI), Damien Roy, 

and Nathan Ng. Waldschmidt spoke on irrationality and 

transcendence methods with an emphasis on the historical 

development of the subject and the construction of 

auxiliary functions. This was a very clear and motivated 

introduction to the theory. Roy’s letures concerned zero 

estimates, Philippon’s criterion for algebraic independence, 

and their application to Gelfond’s problem, showing how 

the two tools can be applied in a specific problem. Ng spoke 

on the analytic theory of Dirichlet L-functions, primes in 

arithmetic progressions, and zeros of the Riemann zeta 

function, covering some background material in preparation 

for the more advanced courses of the second week. 

Each course consisted of five lectures of 80 minutes each. 

The second week of the summer school had the same 

format, consisting of three series of five lectures by Kannan 

Soundararajan, Francesco Amoroso (Caen), and Andrew 

Granville (Montréal). Soundararajan gave a series of lectures 

on L-functions. He discussed probabilistic models, 

the distribution of values, and moments of L-functions. 

In his final lecture Soundararajan presented exciting new 

work on weak sub-convexity for L-functions. In a complementary 

series of lectures Granville gave a comprehensive 

overview of the theory of sums of multiplicative functions. 

He discussed many advances obtained jointly with 

Soundararajan, including their recently introduced notion 

of pretentiousness. Amoroso’s lectures first dealt with Lehmer’s 

problem which asks for a lower bound for the Mahler 

measure of non-zero algebraic numbers which are not roots 

of unity. Then, going to higher dimensions, he defined 

the height of an algebraic sub-variety of an algebraic torus 

and proved several fascinating results, mostly due to him 

and Sinnou David, concerning generalizations of Lehmer’s 

problem in this setting. 

The conference took place in the pleasant setting of Ottawa. 

The student accommodations were well-situated next to the 

lecture rooms and library. In addition, they were near many

famous landmarks of Ottawa including Parliament Hill and 

the Museum of Civilization. All of this created a motivating 

and congenial environment. As the courses were finished 

each day at 3:20 pm, the students had the opportunity 

to review the lectures of the day, ask questions, and hold 

discussions with the lecturers. During the two weeks of 

school the interactions among participants increased both 

academically and socially. In the evenings and weekends 

there were a number of organized and spontaneous activities. 

Some of these included the Canada Day festivities on 

Parliament Hill, biking in Gatineau park, and organized 

soccer matches. There were also a luncheon and two suppers 

organized for the whole group. 

The organizers of this conference were very happy with the 

large number of participants and by their enthusiasm and 

eagerness to learn. In addition, we were pleasantly surprised 

by the diverse representation from 14 countries. We believe 

that this summer school was inspiring and helpful for the 

participants’ research and will lead to further advances 

in the fields of analytic number theory and Diophantine 

approximation. 

Damien Roy 

Summer school in analytic number Theory participants 


99


Seminars 

The Fields Institute hosts several ongoing seminar series 

organized by members of the local mathematics community. 

Some seminars meet on a weekly basis, some even 

more often, while others meet less frequently. However, 

all have a regular program featuring local speakers as well 

as those invited from more distant universities. Seminar 

activities are announced by email sent out by Fields staff 

and on the Institute web site. 

All seminars took place at the Fields Institute. 

Geometry and Model Theory Seminar 2007-08 

Organizers: Patrick Speissegger (McMaster) 

The idea of the seminar is to bring together people from 

the group in geometry and singularities at the University 

of Toronto (including Ed Bierstone, Askold Khovanskii, 

Grisha Mihalkin and Pierre Milman) and the model 

theory group at McMaster University (Bradd Hart, Deirdre 

Haskell, Patrick Speissegger and Matt Valeriote). 

As we discovered in the thematic programs on algebraic 

model theory and on singularity and geometry at the Fields 

Institute in 1996-97, geometers and model theorists have 

many common interests. The goal of this seminar is to 

further explore interactions between the areas. 


Janusz Adamus (Western) 

Vertical components and local geometry of analytic mappings 

Gareth Owen Jones (McMaster) 

Model completeness results for polynomially bounded 

o-minimal structures 

Rasul Shafikov (Western) 

Analytic Geometry questions in Complex Analysis 

Patrick Speissegger (McMaster) 

Transition maps of non-resonant hyperbolic singularities are 

o-minimal 

Mark Spivakovsky (Université Emile Picard, Toulouse) 

The Pierce-Birkhoff conjecture and connected sets in the real 

spectrum 

Guillaume Valette (Toronto) 

Vanishing homology 

Patrick Speissegger 

100 

Fields Analysis Working Group 

July 2007–June 2008 

Organized by Young-Heon Kim and Robert McCann 


In 2007 – 08, the Fields Analysis Working Group (aka 

FAWG) continued to act as an informal venue for local 

researchers in mathematical analysis to describe results 

from the literature and/or work-in-progress organized 

around themes of common interest. This year’s group 

enjoyed nearly thirty lectures on twenty separate occasions, 

often separated by time-out for a working lunch 

on Wednesdays. Approximately half of the lectures were 

presented by student and postdoctoral trainees, including 

thesis research. Many others were devoted to the emerging 

theory concerning smoothness of optimal mappings. 

The highlight was a series of lectures delivered by European 

researcher Alessio Figalli (CNRS, Nice) during a month 

long visit in November-December, in which he described 

Caffarelli’s regularity theory of solutions to the Monge- 

Ampère equation. This lecture series stimulated a fruitful 

and ongoing collaboration between Figalli (PhD 2007) and 

the seminar organizers, as well as independent progress by 

regular participant Almut Burchard giving quantitative 

estimates for the Hölder continuity exponent for optimal 

maps, as she described four months later at FAWG’s final 

meeting of the academic year. As a spin-off, two FAWG 

participants organized a Fields minisymposium on related 

research themes, in conjunction with a Special Session 

on the Calculus of Variations in Physics, Economics, and 

Geometry at the December 2007 meeting of the Canadian 

Mathematical Society in London, Ontario. 


Almut Burchard (Toronto) 

On Caffarelli’s C(1,alpha)-regularity for Monge-Ampere 

equations, What is alpha? 

Paul Lee (Toronto) 

Optimal mass transportation with nonholonomic constraints 

Jim Colliander (Toronto) 


Walid Abou Salem (Toronto) 

On the blind collision of fast solitons 

Robert Jerrard (Toronto) 

Dynamics of topological defects in semilinear hyperbolic PDEs

Hao Li (Toronto) 

Equilibria in a sorting problem 

Tristan Roy (UCLA) 

Global well-posedness for the defocusing cubic wave equation 

Gideon Simpson (Columbia) 

The mathematics of magma migration: nonlinearity, degeneracy, 

and dispersion 

Marina Chugunova (Toronto) 

Spectral properties of the non-self-adjoint operator associated 

with the periodic heat equation 

Abdeslem Lyaghfouri (King Fahd University of Petroleum 

and Minerals) 

Hoelder continuity of solutions to quasilinear elliptic equations 

involving measures 

Kiumars Kaveh (Toronto) 

Isoperimetric inequality, its generalizations and applications 

Larry Guth (Stanford) 

Packing widths and isoperimetric inequalities 

Yuxin Ge (Paris XII and Washington) 

On the 2 -scalar curvature and its application 

Alessio Figalli (CNRS Nice) 

Caffarelli’s Holder regularity theory of Monge-Ampere equations 

Benjamin Stephens (Toronto) 

Parallel transport in Wasserstein Space 

Alessio Figalli (CNRS Nice) 

A mass transportation approach to quantitative isoperimetric 

inequalities 

Young-Heon Kim (Toronto) 

An a priori second order derivative estimate for a Monge- 

Amp\’ere type equation 

Maria Sosio (Toronto) 

An application of the continuity method 

Chad Groft (Toronto) 

Isoperimetric inequalities and universal covers 

Almut Burchard (Toronto) 

Eternal solutions to the Ricci flow on R 2 

Brendan Pass (Toronto) 

Optimal Transportation on Alexandrov Spaces 

Nathan Killoran (Toronto) 

Supports of Extremal Doubly and Triply Stochastic Measures 


Abdeslem Lyaghfouri (King Fahd University of Petroleum 

and Minerals) 

On the Dam Problem with Two Fluids Governed by a Nonlinear 

Darcy’s Law 

Robert McCann 

Toronto Set Theory Seminar 

July 2007–June 2008 

Organizers: Ilijas Farah and Paul Szeptycki (York) 

The Toronto Set Theory Seminar is devoted to the dissemination 

of research on set theory and its applications. 

This includes the research of the core participants: faculty, 

graduate students and post-doctoral students from the University 

of Toronto, York University and the Fields Institute, 

as well as visitors. The seminar continues to offer a venue 

for young mathematicians (students and postdoctoral 

fellows) to be exposed to the frontiers of research in set 

theory and to present their own research. As in years past, 

the seminar attracted many international visitors including 

speakers visiting from Europe and the United States. 

The seminar has long been devoted to all areas of set 

theory and particularly its applications to areas of analysis 

(including the geometry of Banach spaces and C* algebras), 

topology, algebra, and measure theory. This year there 

were a number of talks devoted to combinatorial set theory 

(Balcar, Dobrinen, Elekes, V. Fischer, Moore, Raghavan 

and Schimmerling), descriptive set theory (two series of 

talks by Tornquist), and a diversity of talks devoted to 

applications (Darji, Dodos, Farah, A. Fischer, Pach, Tall and 

Todorcevic). 

The Set Theory Seminar continues to be enriched through 

its association with the Fields Institute. Many speakers 

and visitors were supported directly by the Fields Institute 

through the Set Theory Seminar fund and other sources of 

funding. 


Bohuslav Balcar (Czech Academy of Sciences) 

Refinement properties of countable sets 

Udayan B. Darji (Louisville) 

Generating dense subgroups of some transformation groups 

Natasha Dobrinen (Denver) 

The consistency strength of the tree property at the double successor 

of a measurable cardinal 

101


Pandelis Dodos (Paris and the National Technical University 

of Athens) 

Universality problems and L spaces. 

Marton Elekes (Hungarian Academy of Sciences) 

Partitioning multiple covers into many subcovers 

Arthur Fischer (Toronto) 

PID in models of PFA(S)[S] 

Vera Fischer (York) 

The consistency of b = κ < s for κ arbitrary regular, uncountable 

cardinal. 


The commutant of B(H) in its ultrapowers and flat ultrafilters 

Greg Hjorth (University of Melbourne, UCLA) 

Ends and percolations 

Logan Hoehn (Toronto) 

A model theoretic approach in topology 

Istvan Juhasz (Hungarian Academy of Sciences) 

Discrete subspaces of compacta 

Bernhard Koenig (Toronto) 

Forcing axioms and two cardinal diamonds 

Two ways to construct an ω 2 -Suslin tree from GCH plus additional 

axioms. 

Justin Tatch Moore (Cornell) 

A universal Aronszajn line 

Jan Pachl (Masaryk) 

Ambitable topological groups 

Dilip Raghavan (Toronto) 

A van Douwen mad family in ZFC 

Ernest Schimmerling (Carnegie Mellon) 

Some open questions about L 

Frank Tall (Toronto) 

On a core concept of Arhangel’skii (series of 2 talks) 

More topological applications of PFA(S)[S] 

Stevo Todorcevic (Toronto and CNRS, Paris) 

Unconditional basic sequences in spaces of high density 

Asger Tornquist (Toronto) 

Introduction to Descriptive Set Theory (series of 5 talks) 

Definable Davies’s theorem (2 talks) 

Paul Szeptycki 

102 

Actuarial Science & Financial Mathematics Seminar 

Series Meetings 

September 2007–May 2008 

Organizer: Sebastian Jaimungal (Toronto) 

Actuarial Science and Mathematical Finance (ASMF) are 

two fields which have immense impact in our global economy. 

Understanding how to measure, manage, and value 

the risks embedded in complex financial and insurance 

products is of paramount importance. The mathematical 

sciences play a major role in this enterprise and the synergy 

brought together from mathematics, statistics, computer 

science, engineering and business helps to push the field 

forward. 

The Actuarial Science and Mathematical Finance (ASMF) 

Seminar Series has been running since September 2005. It 

began as a forum for PhD students, post doctoral fellows 

and faculty members to discuss current topics in ASMF, 

partially completed research, as well as reviews of classical 

works and methods. The seminars have always been informal 

to promote discussions, open debate, and allow the 

audience to interact. 

Participation in this series is now much wider and this 

past year showcased talks ranging from stochastic volatility 

modeling to indifference pricing of credit products to 

stochastic fluid models for insurance. The speakers are all 

experts in their respective fields and showcase cutting edge 

research. Several industry professionals regularly participate 

in the event and bring a very valuable grounded real 

world perspective to the discussions and presentations. 


Hans J.H.Tuenter (Ontario Power Generation) 

Expected overshoot in the case of normal variables with positive 

mean 

Andrei Badescu (Toronto) 

Return probabilities of stochastic fluid flows and their use in 

collective risk theory 

Roger Lee (Chicago) 

Implied volatility in relation to realized volatility 

Matheus Grasselli (McMaster) 

Indifference pricing of insurance contracts: stochastic volatility 

and stochastic interest rates 

Sebastian Jaimungal (Toronto) 

Indifference valuation for credit default swaps through a 

structural approach

Erhan Bayraktar (Michigan) 

Pricing Asian options for jump diffusions 

Marcel Rindisbacher (Toronto) 

Dynamic asset-liability management for defined-benefit pension 

plans 

Michael Walker (Toronto) 

Calibration, the timing of defaults, and the marking to market 

of CDO’s 

Michael Ludkovski (Michigan) 

Relative hedging of systematic mortality risk 

Sebastian Jaimungal 

Quantum Information Seminar Series 

September 2007–May 2008 

Organizers: Daniel James, Aephraim Steinberg, Paul 

Brumer and Hoi-Kwong Lo (Toronto) 

As in previous years, the Quantum Information Seminar 

(QIS), run jointly by Fields Institute and the University of 

Toronto’s Centre for Quantum Information and Quantum 

Control (CQIQC – pronounced ‘see-quick’) has had 

a full and stimulating program, with some of the most 

distinguished scientists in the field describing their latest 

discoveries. Quantum information and quantum control 

is a multi-disciplinary field, bringing together mathematicians, 

computer scientists, physicists, electrical and optical 

engineers, nano-scientists, and physical chemists: this 

diversity was fully reflected in the variety of seminars 

presented in this year’s series. The list of speakers included 

visitors from seven different foreign countries (USA, UK, 

Netherlands, Japan, Spain, Sweden and Australia), and six 

different Canadian institutions (NRC, École Polytechnique 

de Montréal, University of Toronto, University of Waterloo, 

University of Montreal and Wilfrid Laurier University). 

The undoubted highlight of this past year was the visit 

in March by Nobel Laureate Roy Glauber of Harvard 

University, one of the founders of quantum optics who, 

in the 1960’s, helped to lay the theoretical foundations for 

today’s on-going quantum revolution. Among various talks 

describing exciting new developments in quantum technologies 

was that given by Jeremy O’Brien who has achieved 

the first ever creation of quantum entanglement on a chip 

– a clear and signal achievement on the road to realizable 

quantum technologies. In February, Joseph Emerson, a 

recent appointment at the Department of Applied Mathematics 

at the University of Waterloo, told us about more 


abstract theoretical issues in quantum mechanics, specifically 

negativity and contextuality as criteria for classicality. 

In summary, 2007-08 was a highly successful year for this 

series, with new ideas exchanged and collaborations created 

between University of Toronto researchers and visitors from 

all over the world. 


Bei-Lok Hu (Maryland and Perimeter Institute) 

Non-Markovian entanglement dynamics of two oubits interacting 

through a quantum field 

Stephen Bartlett (Sydney) 

Identifying phases of matter that are universal for quantum 

computation 

Katya Babourina (Queensland) 

Quantum noise in a nano mechanical Duffing resonator 

Jeremy O’Brien (Bristol) 

Quantum information science with photons on a chip 

Asoka Biswas (Toronto) 

Overlapping resonance in the control of decoherence: N spins 

coupled to a bosonic bath 

Qin Wang (KTH- Royal Institute of Technology) 

Experimentlal demonstration on decoy-state QKD with heralded 

single photon source 

Nicolas Godbout (École Polytechnique de Montréal) 

Shohini Ghose (WLU) 

Robin Williams (Institute for Microstructural Sciences, 

National Research Council) 

Scalable routes to entangled photon pair sources –gated InAs/ 

InP quantum dots in photonic crystal microcavities 

Joseph Emerson (Waterloo) 

Negativity and contextuality as criteria for classicality in discrete 

phase-space and other quasi-probability representations 

of quantum theory 

Yoritoshi Adachi (Osaka) 

Efficient quantum key distribution with parametric downconversion 

source 

Xingxing Xing (Toronto) 

Towards the atom-photon interface in quantum information: 

An ultrabright entangled photon source 

Jonathan Oppenheim (Cambridge) 

Intrinsic decoherence and the destruction of information 

103


Rolando Somma (Perimeter Institute) 

Quantum computing the physical world 

Kirill Shtengel (Riverside) 

Non-Abelian anyon interferometry 

Frédéric Dupuis (Montreal) 

Quantum entropic security and approximate quantum 

encryption 

Marcos Curty (Zaragoza) 

One-way and two-way classical post-processing quantum key 

distribution 

Daniel James 

Algebraic Combinatorics Seminar 

September 2007–June 2008 

Organizers: François Descouens and Nantel Bergeron (York) 

The Algebraic Combinatorics Seminar focused the discussions 

this year on topics related to the Schubert Calculus 

of the affine Grassmannian. The organizer, François 

Descouens, along with a regular attendee, Mike Zabrocki, 

are members of an NSF-funded focused research group that 

is studying the fundamental basis of the affine Grassmannian, 

the k-Schur functions of Lascoux-Lapointe-Morse. 

The main focus of the seminar this year was to develop 

two research ideas which arose during the Summer and 

Fall of 2007 related to commutative and non-commutative 

symmetric functions and their relation to k-Schur functions. 

Nantel Bergeron gave several presentations and 

helped direct the research focus of the group. The seminar 

is attended by roughly 10 graduate students, post-docs and 

other researchers who are interested in these topics in algebraic 

combinatorics. 

This year the research developed in the seminar led to 

two publications by F. Descouens, N. Bergeron and M. 

Zabrocki that were the focus of the talks: arXiv:0804.0944: 

A non-commutative generalization of k-Schur functions and 

arXiv:0806.3046: A Filtration of (q,t)-Catalan numbers 

Five outside guests were invited to speak at the seminar 

and discussed their research on commutative and noncommutative 

symmetric functions, combinatorics and 

the relation to the topics of the seminar. They were: Lenny 

Tevlin (Yeshiva University), Nick Loehr (Virginia Tech), 

Mahir Can (Western), John Irvine (Saint Mary’s), Muriel 

Livernet (Paris XIII). 

Mike Zabrocki 

104 

Colloquium/Seminar in Applied Mathematics 

October 2007–June 2008 

Organizers: Jim Colliander (Toronto), Walter Craig 

(McMaster), Barbara Keyfitz (Fields Institute), Robert 

McCann, Adrian Nachman, Mary Pugh, and Catherine 

Sulem (Toronto) 

The Fields Institute Colloquium/Seminar in Applied Mathematics 

is a monthly colloquium series for mathematicians 

in the areas of applied mathematics and analysis. The intent 

of the series is to bring together the applied mathematics 

community on a regular basis, to present current results in 

the field, and to strengthen the potential for communication 

and collaboration between researchers with common 

interests. The series includes both colloquium talks by 

internationally recognized experts in the field, and less 

formal, more specialized seminars. 

There was a wonderful array of talks on many topics of 

common interest. In particular the following three were 

focussed on several aspects of material science. Robert 

MacPherson presented his recent work on understanding 

the three-dimensional structure of foams and of the grains 

in metal. This unexpected breakthrough uses integral 

geometry and geometric probability. Weinan E presented a 

portion of his research program on multiscale analysis and 

the study of crystalline solids – to what degree can one rigorously 

relate quantum and atomistic models to macroscale 

models of crystals. Finally, Govind Menon presented his 

work on min-driven coarsening; this is a type of two-phase 

coarsening which he has successfully studied using meanfield 

models and methods from probability. 


James Hill (Wollongong) 

Geometry and mechanics of carbon nanotubes and gigahertz 

nano-oscillators 

Yuri A. Kordyukov (Russian Academy of Sciences, Ufa) 

Spectral gaps for periodic Schrödinger operators with magnetic 

wells 

Govind Menon (Brown) 

Min-driven clustering 

Horng-Tzer Yau (Harvard) 

Dynamics of Bose-Einstein condensates 

Jerry Bona (UIC) 

Recent results in nonlinear wave theory 

Kehinde Ladipo (Houston) 

Finite element analysis of fluid motion in conical diffusers

Reinhard Illner (Victoria) 

From Fokker-Planck type kinetic traffic models to stop-and-go 

waves in dense traffic 

Isom Herron (Rensselaer Polytechnic Institute) 

A new look at the principle of exchange of stabilities 

Laurette Tuckerman (PMMH-ESPCI, Université Pierre et 

Marie Curie) 

Patterns in turbulence 

Jun Zhang (NYU) 

Free-moving boundaries interacting with thermal convective 

fluids 

Weinan E (Princeton) 

Mathematical theory of solids: From atomic to macroscopic 

scales 

Robert MacPherson (IAS) 

The geometry of grains 

Michel Chipot (Zürich) 

Exponential rate of convergence for the solution of elliptic 

problems in strips 

Walter Craig 

Toronto Probability Seminar 

October 2007–June 2008 

Organizers: Bálint Viraq and Benedek Valkó (Toronto) 

For the fifth consecutive year, the Toronto Probability 

Seminar has been meeting in the Fields Institute Library 

at 4pm on Mondays. This multidisciplinary seminar had 

speakers and audience members from the areas of mathematics, 

statistics, physics, engineering, chemistry, and 

computer science. 

The main focus is current research in theoretical probability. 

This year’s seminar speakers were some of the top local 

and international researchers in the area. Speakers came 

from a wide variety of institutions including Cambridge 

University, Microsoft Research and the University of British 

Columbia. 

Manjunath Krishnapur talked about random analytic functions, 

Brian Rider, Bálint Virag and Benedek Valkó gave 

talks on scaling limits of random matrices, James Mingo 

presented results on free probability. Omer Angel gave 

two presentations: one on random sorting networks and 

another on random spanning trees. Gidi Amir discussed 

a problem about excited random walks, Gabor Pete gave a 


talk on critical percolation and Mathieu Merle on Super- 

Brownian motion. Balázs Szegedy talked about finding 

randomness in large graphs, Mate Matolcsi discussed the 

polarization problem and Nathanael Berestycki presented 

results on coalescent processes. 


Gidi Amir (Toronto) 

Excited random walk against a wall 

Omer Angel (Toronto) 

Minimal spanning trees revisited 

The oriented swap process 

Nathanael Berestycki (Cambridge) 

The speed of coming down from infinity for coalescent processes 

Manjunath Krishnapur (Toronto) 

From random matrices to random analytic functions 

Mate Matolcsi (Renyi Institute of Mathematics) 

The real polarization problem 

Mathieu Merle (UBC) 

Voter, Lotka-Volterra models and super-Brownian motion 

James Mingo (Queen’s) 

Free cumulants: First and second order 

Gabor Pete (Microsoft Research) 

The exact noise and dynamical sensitivity of critical percolation, 

via the Fourier spectrum 

Brian Rider (Colorado at Boulder) 

Diffusion at random matrix theory’s hard edge 

Balázs Szegedy (Toronto) 

Forcing randomness 

Benedek Valkó and Bálint Virag (Toronto) 

The Brownian Carousel 

Bálint Virag 

High Energy Physics/String Theory Seminar 

High Energy Physics/String Theory Seminar 

Nov. 5 2007- Mar. 10 2008 

Organizers: Erich Poppitz, Kentaro Hari and Amanda Peet 


The series was financially supported by the Fields Institute, 

the Department of Physics and the Department of 

Mathematics at the University of Toronto, as well as by the 

Canadian Institute for Advanced Research. 

105



Michael Schultz (Pennsylvania) 

String Junctions, Abelian Fibrations and Flux/Geometry 

Duality 

Yang-Hui He (Merton College, Oxford) 

Triadophilia: a special corner of the landscape 

Josh Guffin (UIUC) 

Deformed Quantum Cohomology and (0,2) Mirror Symmetry 

Daniel Jafferis (Rutgers) 

Fragmenting 4-branes and q-deformed Yang-Mills 

Boris Pioline (Paris VI et VII) 

Quantum attractor flows and black hole partition functions 

Thomas Levi (NYU) 

Black Hole Microstates: From D-branes to Foam 

106

Centre for Mathematical Medicine 

Directors: Amit Oza (Princess Margaret Hospital and University 

of Toronto) and Sivabal Sivaloganathan (Waterloo) 

Program Coordinator: Irwin Pressman (Carleton) 

The activities of the Centre for Mathematical Medicine 

(CMM) have continued to escalate over the past year with 

a number of short term visitors, working group activities, 

seminars, and workshops, culminating in a highly successful 

international conference and summer thematic 

program. As always, there is a latent inertia when two such 

traditionally disparate fields such as mathematics and 

the biomedical sciences are brought together. However, it 

appears that there is a groundswell of interest, and the goal 

for CMM this coming year will be to try to engage more 

mathematicians in the stimulating current problems in 

the biomedical sciences as this interdisciplinary field of 

research gains momentum. Mathematical medicine and 

mathematical biology are poised to take centre stage in 

biomedical research. If mathematicians do not become 

actively engaged in these interdisciplinary endeavors, they 

will not be part of the advances and discoveries that surely 

lie ahead. 

The Centre for Mathematical Medicine (CMM) was 

established in 2005 and since that time has been housed 

and maintained at the Fields Institute for Research in 

Mathematical Sciences. Thanks principally to the backing 

and financial support of Fields, plus other institutional and 

private sources, CMM has significantly expanded its activities 

this year. The work of earlier years is now bearing fruit. 

The purpose of the Centre, as described in our vision statement, 

is threefold: 


• foster collaborative, interdisciplinary research in the 

medical sciences 

• stimulate and engage graduate students and young 

researchers 

• teach at undergraduate and graduate levels. 

We are on track to achieving these goals. 

A relationship has developed with The Vanderbilt Integrative 

Cancer Biology Center, a part of the Integrative Cancer 

Biology Program (ICBP) of the U.S. National Cancer 

Institute (NCI). They joined us to present their “Summer 

School” at Fields. We hope that this is the beginning of an 

ongoing partnership. 

Another contribution of CMM has been to introduce 

colleagues to some serious and important challenges in 

Biology and Medicine where Mathematics plays a role. 

There are significant opportunities for new, cooperative 

and cross-disciplinary research. We quote Joel Cohen in 

PLOS BIOLOGY: “Mathematics is biology’s next microscope, 

only better; Biology is mathematics’ next physics.” 

We also quote from the National Academies’ publication, 

Mathematics and 21 st Century Biology: “The main push in 

Biology during the coming decades will be toward an increasingly 

quantitative understanding of biological function; the 

rate at which progress occurs will depend on a deeper, effective 

implementation of quantitative methods and a quantitative 

perspective within the biological sciences. The success of 

this transformation will depend in part on the creation and 

nurturance of a robust interface between biology and mathematics, 

which should become a top priority of science policy.” 

“The nature of the field of biology is in dramatic flux due to a 

surge of new sources of data, access to high-performance computing, 

increasing reliance on quantitative research methods, 

and an internally driven need to produce more quantitative 

and predictive models of biological processes. The growing 

infusion of mathematical tools and reasoning into biology 

may therefore be expected to further transform the life sciences 

during the decades ahead.” 

Significant Activities 

Our significant new activities, whose organizational aspect 

took up most of the past year, include: 

107


• The hosting of the Society for Mathematical Biology 

(SMB) Conference with over 350 registrants, 50 talks, and 

15 mini-symposia. July 30-August 2, 2008 

• The development of a Thematic Program on Mathematical 

and Quantitative Oncology including creation and 

delivery of a series of workshops and graduate courses at 

Fields during the Summer 2008 

July 2-4, 2008 

Workshop on Growth and Control of Tumors: Theory and 

Experiment 

August 2-6, 2008 

VICBC Summer School on Integrative Cancer Biology 

“Current Challenges in Oncology, through the Mathematical 

Looking Glass” 

August 25-27, 2008 

Workshop on Quantitative Cancer Modeling: Mathematical 

Models, Imaging and Bioinformatics 

Graduate Student courses 

Two Graduate Student courses delivered at Fields during the 

Summer 2008 are 

• Course on Introduction to Mathematical Oncology 

• Course on Medical Image Processing 

2007-08 Seminar and Lecture Series 

Many of the seminars and lectures can be heard (or slides 

seen) on the Fields web-site. 

November 30, 2007 

Dr. Raghu Raghavan (Therataxis, LLC, Baltimore): Aristotelian 

physics and brain disease. 

The delivery of therapeutics directly into the brain across 

the blood-brain barrier is modeled by using frictiondominated 

continuum mechanics, kinetic theory, and the 

connection between diffusion and random walk. 

January 25, 2008 

David Earn (McMaster) 

Lessons from death: Epidemiological insights from historical 

mortality records. 

January 25, 2008 

David Fisman (Hospital for Sick Children) 

‘Old Timey Diseases’ in the here and now: Current status of 

whooping cough in Toronto. 

Held at the Fields Institute 

108 

In the mid-twentieth century, many thought that infectious 

diseases would soon be a thing of the past. Penicillin had 

almost vanquished major bacterial infections, while mass 

vaccination had dramatically reduced the prevalence of 

other diseases. Many medical students were even advised 

not to bother specializing in infectious diseases! However, 

the past few decades have seen a resurgence of infectious 

diseases old and new. For instance, SARS and avian 

influenza have emerged (seemingly) out of nowhere, while 

diseases once thought to be on their way out (mumps, 

pertussis, measles) have invited themselves back in, often 

through suboptimal vaccination. Similarly, diseases that 

were no longer thought to represent a risk (plague, smallpox) 

are now seen as potential bioterrorist weapons. This 

comeback, together with growing recognition of the role 

that mathematical modelling can play in understanding 

infectious disease dynamics and informing public health 

policy, are fuelling growing interest in epidemiological 

modelling. On 25 January, for the first talks of the 

2007-2008 Centre for Mathematical Medicine Seminar 

Series, David Earn and David Fisman described research in 

epidemic modelling that is helping to fill this need.

In Lessons from death: Epidemiological insights from historical 

mortality records, Earn summarized his group’s 

exhaustive efforts to digitize data from the London Bills 

of Mortality, describing all causes of death in London 

from the 17 th century onward, particularly in the “Great 

Plague of 1665.” This epidemic, traditionally thought to 

have been caused by bubonic plague (which still exists 

today), killed 20% of London’s population. Earn presented 

intriguing parish-level spatio-temporal data, showing 

how the plague started on the outskirts of London, and 

gradually encroached upon the city centre. By parameterizing 

differential equation models of plague transmission 

using data from the Bills of Mortality, Earn showed that 

the Great Plague was, surprisingly, not very transmissible, 

despite its high case fatality rate. In this way, it had much in 

common with smallpox, SARS, and the 1918 “Spanish Flu” 

pandemic, all of which had major impacts despite their low 

transmissibility. 

In a similar vein, Fisman started his seminar “Old timey 

diseases” in the here and now: Current status of pertussis 

(whooping cough) in Toronto by outlining a number of 

historically prevalent diseases that are now staging a comeback, 

such as measles, mumps, and pertussis. For instance, 

in Toronto there was a dramatic and puzzling increase in 

the number of positive lab tests for pertussis in 2005. In the 

years preceding, new methods of testing were also introduced. 

Was the increase in test positives due to an increase 

in pertussis transmission, or to the change in testing? To 

answer this question, Fisman statistically analyzed time 

series data compiled by Toronto labs. The analysis pointed 

to a nonlinearity – changing testing technology combined 

with a heightened response of health care providers to an 

increase in test positives – as the major factor in the recent 

surge. However, part of the increase may still be attributable 

to periodic peaks in epidemic activity that characterize 

pertsussis transmission and that can be captured by mathematical 

models. 

Chris Bauch 


Donald B Plewes (Sunnybrook Health Sciences Centre, 

University of Toronto) 

Micron scale motion detection by magnetic resonance imaging: 

Principles and applications. 

Magnetic Resonance Imaging (MRI) is widely used 

throughout clinical medicine today with applications in 

cancer, basic neuroscience, cardiovascular disease, drug 


development and pre-clinical research. It has achieved this 

due to its non-invasive nature coupled with the rich array 

of potential NMR signals that can be applied to biological 

problems. 


Lindi Wahl (Western) 

Recurrent viral infection: Why recurrence doesn’t need a trigger 

In chronic viral infection, low levels of viral replication 

are maintained over long periods, but may be punctuated 

by bursts of high viral production and release. A model 

was discovered that incorporates the contributions of both 

cytotoxic T lymphocytes (the killer cells of the immune 

system) and antibodies. It suggests that for recurrent viral 

infections, no exogenous trigger is necessary to provoke an 

episode of reactivation. 


Beni Sahai (Cadham Provincial Lab, Manitoba) 

Pathway to T cell memory 

The immunological memory develops and persists in 

forms of specific T and B cells that arise as products of 

antigen-driven clonal expansion through an intricate 

pathway regulated by homeostasis. Insights were provided 

into unique mechanisms that lead to development of T cell 

memory and its persistence in the absence of antigen. 

April 18, 2008 

Leon Glass (McGill) 

Cardiac arrhythmias – From simple models to the clinic. 

A sterling instance of our activity this year was the talk 

by Professor Leon Glass, McGill University. Glass is a 

PhD in Chemical Physics, an author of 5 books and 200+ 

papers, a Professor of Physiology and an endowed Chair 

in Cardiology. He is an expert and pioneer in applications 

of Nonlinear Dynamics to problems in physiology. He 

had a standing-room-only audience including students 

bussed in from out-of-town Universities. The human heart 

can sustain a large number of different types of abnormal 

cardiac rhythms – called cardiac arrhythmias. A challenge 

facing experimentalists and theoreticians is to derive sufficient 

understanding of these abnormal rhythms in order 

to treat patients with heart disease. Simple theoretical and 

biological models often display complex rhythms that can 

be analyzed using mathematical and physical approaches. 

109


One might want to try to analyze the ECG traces to predict 

oncoming cardiac events. It’s not so easy unless you are 

a cardiologist. Glass discussed both a clinical and basic 

science approach to sudden cardiac death. The electrical 

activity of the heart as well as rhythm changes that give 

abnormal beats – runs of which can precede death – were 

described. One question is “can we predict high risk of 

sudden cardiac death from an analysis of the waveforms?” 

Cardiologists can prevent sudden cardiac death in many 

cases with an implantable cardiac defibrillator that can 

often terminate undesirable rhythms. This instrument 

is expensive and installing it is sometimes problematic. 

Another question is “how do we choose the optimal group 

to receive this defibrillator?” 

July 7, 2008 

Graeme Wake (Massey University, Auckland) 

Modelling of cancer treatment 

A model describing the complexities of the responses of 

tumor cells over time to both anticancer drugs and radiation 

was described. This may allow individualization of 

cancer therapy. Models for the response of human tumors 

to chemotherapy and radiotherapy with mathematical 

equations that may be perturbed to predict treatment 

effects were discussed. 

July 9, 2008 

Graeme Wake (Massey University, Auckland) 

A model for phenotype change in a stochastic framework 

In some species, an inducible secondary phenotype will 

develop some time after the environmental change that 

evokes it. Stochastic predator-prey models in which the 

prey has a fixed initial energy budget trade off reduction in 

the probability of predation against increase in the energy 

required to maintain a phenotype with improved defense. 

Wake gave a stimulating example of grass competition with 

clover in New Zealand sheep farms and the effects of the 

clover percentage on the sheep. 

110 

Collaborative Research Projects 

CMM is also involved in several ongoing collaborative 

research projects. 

Hydrocephalus and Trauma: A Novel Synergistic Approach to 

Brain Biomechanics 

We are developing a comprehensive mathematical model 

capable of predicting the brain’s response in different loading 

situations regularly encountered by neurosurgeons. The 

application is to the prediction of the optimal shunt positioning 

in hydrocephalic patients. We also address clinical 

conditions such as syringomyelia, with a view to predicting 

the evolution of a syrinx in the spinal cord to suggest effective 

intervention strategies. Participants: James M. Drake 

(Hospital for Sick Children), Miles Johnston (Sunnybrook 

& Women’s Hospital), Siv Sivaloganathan (CMM & Waterloo), 

Mohammed Kohandel (Waterloo), Guisseppe Tenti 

(Waterloo). 

A Workshop on Brain Biomechanics: Mathematical Modelling 

of Hydrocephalus and Syringomyelia was held at Fields 

on July 27, 2007 with over 40 participants. 

Brain Response to Static and Dynamic Loading 

Marc Del Bigio has established a state of the art experimental 

facility at his lab in Manitoba. We are developing 

a quasilinear viscoelastic model of the brain using his 

data. An MRI machine adapted for Magnetic Resonance 

Elastography (MRE) will be available shortly and the elastic 

parameters found by MRE will be used in the construction 

of a new biomechanical model capable of correctly predicting 

the dynamics of soft tissues and response to treatment 

interventions. 

Participants: Marc Del Bigio (Manitoba), Stefan Cenkowski 

(Manitoba), James M. Drake (Hospital for Sick Children), 

Corina Drapaca (Mayo Clinic), Siv Sivaloganathan (CMM 

& Waterloo). 

Dynamics of Multi-Modal, Anti-Angiogenic, Antivascular 

and Cytotoxic Therapies: Potential for Significant Clinical 

Impact 

The effects of antiangiogenic therapy on tumour vasculature 

are studied with the goal to develop dynamic 

combination therapies that respond to ever-changing 

tumour micro-environment under therapy. There is currently 

scant pre-clinical or clinical evidence on which one 

can base decisions about optimal combinations of antiangiogenic 

and cytotoxic therapies.

Participants: Michael Milosevic (PMH), David Jaffrey 

(OCI), Mehran Kardar (MIT), Mohammed Kohandel 

(Waterloo), Siv Sivaloganathan (CMM & Waterloo), Rae 

Yeung (Toronto). 

Mohammed Kohandel, Siv Sivaloganathan and Michael 

Milosevic of CMM were awarded an NSERC CHRP grant 

of $430,000 over three years for their project Dynamics of 

multi-modal anti-angiogenic, anti-vascular and cytotoxic 

therapies: potential for significant clinical impact. Their 

recently published paper (with M. Khardar of MIT) 

entitled Dynamics of tumour growth and combination of 

anti-angiogenic and cytotoxic therapies has been selected as 

a “Featured Article” by the editors and reviewers of Physics 

in Biology & Medicine for “..its novelty, high level of interest 

and potential impact on future research.” 

Graduate students 

There are many graduate students in Mathematical Medicine 

at the University of Waterloo and Princess Margaret 

Hospital. They include Rudy Gunawan, Gibin Powathil, 

Sean Speziale, Colin Turner, Kathleen Wilkie, Colin 

Phipps, Herbert Tang, Antonio Sanchez, Maryam Rouhani 

and Hamid Molavian (postdoc). 

Working groups 

1) Digital Pathology 

2) Hospital Bed Allocation and Emergency Response 

3) Epilepsy Prediction and Control 

These working groups are interdisciplinary, composed of 

mathematical scientists and clinician/scientists and focused 

on problems of current clinical interest. 

Irwin Pressman 


111


Joint Institute Initiatives 

112 

Canadian Mathematical Society Winter 

2007 Meeting 

December 8-10, 2007 

Held at the Hilton Hotel, London, Ontario 

Meeting Director: Rick Jardine (Western) 

Local Arrangements: David Riley (Western), 

Gertrud Jeewanjee (CMS, ex-officio) 

The meeting welcomed approximately 410 participants. 

Following the usual format of the CMS Winter Meeting, 

the program included a wide variety of special sessions and 

plenary and prize lectures. 

Prize Lectures: 

CMS Coxeter-James Lecture: 

Vinayak Vatsal (UBC) 

Special values of L-functions modulo p 

CMS Doctoral Prize: Lap Chi Lau (Chinese University of 

Hong Kong) 

On approximate min-max theorems for graph problems 

CMS Adrien Pouliot Address: Richard Nowakowski (Dalhousie) 

Can you repeat that, sir? 

Plenary Lectures: 

Marcelo C. Borba (UNESP – Sao Paulo State University) 

Modeling, projects and internet: aternatives to undergraduate 

basic mathematics courses 

Erich Kaltofen (North Carolina State) 

Expressing a fraction of two determinants as a determinant 

Mikhail Kapranov (Yale) 

Algebro-geometric models for the spaces of unparametrized 

paths 

Giovanni Landi (Trieste) 

Dirac operators on noncommutative manifolds 

Blaine Lawson (SUNY – Stony Brook) 

Projective hulls, projective linking, and boundaries of analytic 

varieties 

Seth Lloyd (MIT) 

Quantize clocks, not gravity 

Otmar Venjakob (Heidelberg) 

Are zeta-functions able to solve Diophantine equations? 

Special Sessions: 

Algebraic Combinatorics, Representations and Geometry 

Organizers: Lex Renner (Western) and Benjamin Steinberg 

(Carleton) 

Algebraic Stacks 

Organizer: Ajneet Dhillon (Western) 

Algorithmic Challenges in Polynomial and Linear Algebra 

Organizer: Stephen Watt (Western) 

Calculus of Variations in Physics, Geometry and Economics 

Organizers: Robert McCann and Benjamin Stephens 


Combinatorics and its Applications to Mathematical 

Physics 

Organizers: Michael Gekhtman (Notre Dame) and Michael 

Shapiro (Michigan State) 

Complex Analytic Geometry 

Organizers: Tatyana Foth (Western), Finnur Larusson 

(Adelaide) and Rasul Shafikov (Western) 

Error Control Codes, Information Theory and Applied 

Cryptography 

Organizers: Aiden Bruen (Calgary) and David Wehlau 

(Queen’s; RMC) 

Graph Theory 

Organizers: Sebastian Cioaba (UC-San Diego), Stephen 

Kirkland (Regina) and Claude Tardif (RMC) 

History and Philosophy of Mathematics 

Organizers: Tom Archibald (SFU) and Deborah Kent 

(Hillsdale College) 

Homotopy Theory 

Organizer: Kristine Bauer (Calgary) 

Iwasawa Theory 

Organizers: Manfred Kolster and Romyar Sharifi (McMaster) 

Mathematical Applications of Category Theory 

Organizers: F. William Lawvere (SUNY Buffalo) and Walter 

Tholen (York) 

Mathematics of Finance 

Organizers: Matt Davison, Rogemar Mamon and Mark 

Reesor (Western)

Non-Commutative Geometry 

Organizer: Masoud Khalkhali (Western) 

Nonlinear Wave Equations and Applications 

Organizers: Walter Craig (McMaster) and Catherine Sulem 


Quantum Information Theory in Quantum Gravity 

Organizers: David Kribs (Guelph) and Fotini Markopoulou 

(Perimeter Institute) 

Contributed Papers 

Organizer: Tatyana Foth (Western) 

In addition, the following session in Mathematics Education 

took place: 

Mathematical Imagination 

Organizer: George Gadanidis (Western) 

Details and abstracts of the talks can be found on the web 

site of the meeting, at www.cms.math.ca/Events/winter07/ 

Sponsors: 

Support from the following institutions was gratefully 

acknowledged: 

le Centre de Recherches Mathématiques 

The Fields Institute 

MITACS 

Pacific Institute for the Mathematical Sciences 

University of Western Ontario 

- Department of Mathematics 

- Faculty of Education 

- Faculty of Science 

- Research Western 

- Department of Applied Mathematics 

Gertrud Jeewanjee 

Joint Meeting of the Statistical Society of Canada and 

the Société française de statistique 


Held at the Ottawa Congress Centre, Ottawa 

Organizers: Bruno Rémillard (HEC Montreal) and Marc 

Hallin (ULB, Belgium) (Co-Chairs of the Program Committee), 

and Pierre Lavallée (Statistics Canada) (Chair of 

the Local Arrangements Committee) 

This, the 36 th Annual Meeting of the SSC and the 40 th 

Annual Meeting of the SFdS and the first to be held 

jointly by the two sister societies, was a huge success in 

terms of participation and scientific program. Nearly 840 


participants registered. There were more than 500 communications 

distributed in 109 sessions, including 4 plenary 

sessions, 4 statutory invited paper sessions, 44 invited sessions, 

3 poster sessions, and 2 case studies. 

The first plenary session on Monday was the SSC Presidential 

Invited Address. Paul Embrechts (ETH Zurich) talked 

about Statistics and Quantitative Risk Management. He 

introduced the audience to risk estimation, risk aggregation, 

risk diversification and contagion. Given the recent 

financial events, this topic is likely to be hot for many 

years to come. Next, the Lucien Le Cam Address was given 

by Richard Gill (Leiden), who entertained the audience 

with his talk Hunting Serial Killer Nurses with Statistics. 

He explored the role of statistics in the conviction of a 

presumed serial killer in the Netherlands. The third plenary 

session, the SFdS Presidential Invited Address, was given 

by Davy Paindaveine (Université Libre de Bruxelles) who 

was the recent winner of the Gottfried E. Noether Young 

Scholar Award of the American Statistical Association. 

His talk was entitled Invariant Methods for Independent 

Component Models. Finally, the last plenary talk was the 

Gold Medal Award Address of the SSC. The winner, Don 

McLeish (Waterloo) told the audience about his Personal 

Random Walk, from Martingales to Monte Carlo methods. 

He gave many examples of the fruitful relationship between 

theoretical developments in probability and computational 

advances. 

As in all SSC Annual Meetings, many sessions were 

organized by the SSC Sections in Biostatistics, Industrial 

Statistics, Survey Methods and Probability. In addition, several 

invited paper sessions were organized by the SFdS on a 

variety of topics such as data confidentiality, the collection 

of ethnic data in Canada and France, and applications 

of statistics to the environment. One session was also 

presented in honour of Professor Denis Bosq, who retired 

recently. There were also two sessions in memory of André 

Dabrowski, including an emotional talk by one on André’s 

most active collaborators, Harold Dehling (Bochum). 

The success of the joint meeting is partly due to the generosity 

of the following sponsors: Centre de recherches 

mathématiques, the Fields Institute, Institut des sciences 

mathématiques du Québec, MITACS, National Program on 

Complex Data Structures, Pacific Institute for the Mathematical 

Sciences, Canadian Heritage, Carleton University, 

French Embassy in Canada, SAS ® , Statistical Society of 

Ottawa, Statistics Canada, and University of Ottawa. 

Bruno Rémillard 

113


Second Canada-France Congress 2008 


Held at l’Université du Québec à Montréal 

Organized by Canadian Applied and Industrial Mathematics 

Society (CAIMS), Canadian Mathematical Society 

(CMS), Centre de Recherches Mathématiques (CRM), 

Fields Institute, Institut des Sciences Mathématiques (ISM), 

Mathematics of Information Technology & Complex 

Systems (MITACS), Pacific Institute for the Mathematical 

Sciences (PIMS), Société de Mathématiques Appliquées 

et Industrielles (SMAI), Société Mathématique de France 

(SMF), Université du Québec à Montréal (UQAM). 

Scientific Directors: Octav Cornea (Université de Montréal), 

Nassif Ghoussoub (UBC), Francois Loeser (École 

normale supérieure) 

Local Arrangements: Christiane Rousseau (chair, Montréal), 

Alexandra Haedrich (ISM), Gertrud Jeewanjee 

(CMS), Jo-Anne Rockwood (MITACS) 

The program included a wide variety of scientific sessions; 

plenary, prize and public lectures; symposia; workshops; 

and a poster session. The CMS student committee organized 

a workshop and the MITACS student committee 

organized “Math en jeu,” a computer game competition. 

NSERC presented two workshops. 

The Congress welcomed approximately 820 participants. 

Plenary Lectures: (in alphabetical order) 

Yves André (CNRS-ENS, Paris) 

Slope filtrations and their metamorphoses 

Olivier Biquard (Strasbourg) 

Conformal geometries and Einstein metrics 

Luc Devroye (McGill) 

Random trees 

Andrew Granville (Montréal) 

Pretentiousness in analytic number theory 

Alice Guionnet (CNRS-ENS, Lyon) 

Topological expansions and applications 

Rick Kenyon (Brown) 

Limits of Dimer models 

Gérard Laumon (CNRS-Orsay) 

Hitchin fibration and fundamental lemma 

Eric Sere (Paris-Dauphine) 

Variational problems in relativistic quantum chemistry 

114 

Jean-Pierre Serre (Collège de France) 

Le groupe de Cremona 

Nicole Tomczak-Jaegermann (Alberta) 

Random embeddings and approximation and other highdimensional 

geometric phenomena 

Nizar Touzi (CREST-Paris) 

Probabillistic numerical methods for fully-nonlinear PDEs 

Jianhong Wu (York) 

Disease outbreaks and outbreaks of disease modeling 

Prize Lectures: 

CAIMS Cecil Graham Doctoral Dissertation Award – Alysson 

M. Costa (Sao Paulo) 

Models and algorithms for two network design problems 

CAIMS Research Prize – Alan George (Waterloo) 

Thirty Years of progress in the solution of large sparse systems 

CMS Excellence in Teaching Award – Edward Bierstone 


Reflections on teaching undergraduate mathematics 

CMS Krieger-Nelson Prize – Izabella Laba (UBC) 

Geometric measure theory and arithmetic combinatorics 

CMS Jeffery-Williams Prize – Martin Barlow (UBC) 

Random walks in symmetric random environments 

Public Lecture 

Yvan Saint-Aubin (Montréal) 

Désordre et beauté / Disorder and beauty 

SCIENTIFIC SESSIONS 

The congress hosted 28 parallel scientific sessions, covering 

a wide range of mathematical research interests. The sessions 

and their organizers were as follows: 

Algebraic Combinatorics 

Organizers: Christophe Hohlweg, Franco Saliola (UQAM) 

Algebraic Groups and Related Topics 

Organizers: Philippe Gille (CNRS-ENS, Paris), Zinovy 

Reichstein (UBC) 

Algebraic Topology 

Organizers: Alejandro Adem (UBC), Bob Oliver (Paris 

XIII) 

Analytic Number Theory 

Organizers: Philippe Michel (Montpellier), Ram Murty 

(Queen’s)

Arithmetic Geometry and Number Theory 

Organizers: Gaëtan Chenevier (CNRS, Paris XIII), Henri 

Darmon (McGill) 

Automorphic Forms 

Organizers: Stephen Kudla (Toronto), Colette Moeglin 

(CNRS-IMJ) 

Complex Analysis and Operator Theory 

Organizers: Emmanuel Fricain (Lyon), Javad Mashreghi 

(Laval), Thomas Ransford (Laval) 

Complex Dynamical Systems 

Organizers: Xavier Buff (Toulouse), Tan Lei (Cergy- 

Pontoise), Misha Lyubich (Toronto) 

Financial Mathematics 

Organizer: Tom Salisbury (York) 

Geometric and Nonlinear Analysis 

Organizers: Pengfei Guan (McGill), Emmanuel Hebey 

(Cergy) 

Industrial Fluid Mechanics 

Organizers: Neil Balmforth (UBC), Jean Frédéric Gerbeau 

(INRIA), Bertrand Maury (Paris Orsay) 

Kinetic Methods in Partial Differential Equations 

Organizers: François Castella (Rennes), Reinhard Illner 

(Victoria) 


Organizers: Michèle Artigue (Paris), Bernard Hodgson 

(Laval) 

Model Theory and Applications to Geometry 

Organizers: Zoé Chatzidakis (CNRS), Patrick Speissegger 

(McMaster) 

Non-Commutative Geometry and K-Theory for Operator 

Algebras 

Organizers: Alain Connes (Collège de France; IHES), 

George Elliott (Toronto), Andrew Toms (York) 

Nonlinear Dynamics in Life Sciences 

Organizers: Jaques Bélair (Montréal), Pascal Chossat 

(CIRM-Marseille), Fahima Nekka (Montréal), Jianhong 

Wu (York) 

Numerical Analysis for Hyperbolic Systems 

Organizers: Paul Arminjon (Montréal), Marc Laforest 

(Ecole Polytechnique de Montréal), Emmanuel Lorin 

(UOIT) 


Partial Differential Equations 

Organizers: Henri Berestycki (Paris), Robert Jerrard 


Probability 

Organizers: Martin Barlow (UBC), J.F. Le Gall (Paris 

XI-ENS), Edwin Perkins (UBC), Wendelin Werner (Paris 

Orsay) 

Scientific Computing 

Organizers: Christine Bernardi (CNRS-Paris VI), Anne 

Bourlioux (Montréal), Brian Wetton (UBC) 

Set Theory and its Applications 

Organizers: Alain Louveau (Paris VI), Stevo Todorcevic 

(Toronto; Paris Dauphine) 

Statistics 

Organizers: Yannick Baraud (Nice), Boris Levit (Queen’s) 

Stochastic Processes in Evolution, Ecology and Genetics 

Organizers: Don Dawson (Carleton), Sylvie Méléard (Ecole 

Polytéchnique-Paris X) 

Symplectic and Contact Geometry 

Organizers: Emmanuel Giroux (CNRS-ENS Lyon), Yael 

Karshon (Toronto) 

Topology, Knots and Related Fields 

Organizers: Michael Boileau (Toulouse), Steven Boyer 

(UQAM) 

Variational and Numerical Methods in Geometry, Physics 

and Chemistry 

Organizers: Lia Bronsard (McMaster), Eric Cances (ENPC), 

Maria J. Esteban (CNRS-Paris Dauphine) 

Women in Mathematics 

Organizers: Maritza Branker (Niagara), Barbara Keyfitz 

(Fields Institute), Marie-Françoise Roy (Rennes) 

CAIMS SyMPOSIA 

Asymptotic Analysis of Localized Patterns in PDEs 

Organizers: David Iron and Theodore Kolokolnikov (Dalhousie) 

Canadian Symposium on Fluid Dynamics 

Geophysical Fluid Dynamics (Organizer: Lucy Campbell) 

T urbulence and Transition (Organizer: Lennaert van 

Veen) 

Computational Fluid Dynamics (Organizer: John Bowman) 

115


Modeling Fluid-Structure Interaction in Naval Architecture 

Organizer: Serguei Iakovlev (Dalhousie) 

Models for Transmission of Communicable Diseases 

Organizers: Fred Brauer (UBC) and Pauline van den 

Driessche (Victoria) 

Models of Motion in Biology 

Organizer: Dan Coombs (UBC) 

New Software for the Numerical Solution of Differential 

Equations 

Organizers: Paul Muir (St. Mary’s) and Ray Spiteri (Saskatchewan) 

Singular Perturbations and the Ginzburg-Landau model 

Organizers: Stan Alama and Lia Bronsard (McMaster) 

CAIMS ARTHUR BEAUMONT DISTINGUISHED 

SERVICE AWARD 

Ken Jackson (Toronto) 

MITACS MENTORSHIP AWARDS 

Kim McAuley (Queen’s) 

Tamás Terlaky (McMaster) 

Gertrud Jeewanjee 

116

AARMS Activities 

AARMS Summer School 

July 16–August 10 2007 

Held at Dalhousie University 

The 2007 AARMS Summer School was held in the Department 

of Mathematics and Statistics, Dalhousie University, 

Halifax, Nova Scotia, from July 16 to August 10. The Director 

of this year’s School was Pat Keast, with assistance from 

Renzo Piccinini. There were 27 students attending classes. 

These came from Alberta, Brazil, China, Germany, Italy, 

Newfoundland and Labrador, New Brunswick, Nova Scotia, 

Ontario, Romania, and Spain. Several students were attending 

their second Summer School, and one has attended all 

three Dalhousie Schools. Also, one third of the students 

were women. The classes taught were Polynomials (Instructor: 

Ed Barbeau, Toronto); Statistical Numerical Integration 

(Instructor: Alan Genz, Washington State); Mathematical 

Models in Ecology and Evolution (Instructor: Frithjof 

Lutscher, Ottawa); and Introductions to Number Theory 

(Instructor: Alf van der Poorten, Sydney). The students, as 

in previous years, were very gregarious and the atmosphere 

at meal times, in the dining hall of Howe Hall residence, 

was always wonderful. (Except for a few days when one 

student was mis-diagnosed as having mumps, leaving the 

other students a little bit nervous until the all clear was 

given!) 

As in previous Summer Schools, students had to find their 

own way to Halifax, where accommodation and meals were 

provided by the School. There were two social events. On 

the first Monday, the Graduate Student Society hosted a 

dinner-time barbecue, which was a great success. This was 

held on the balcony of the Chase Building, easily the best 

asset of the building, especially when the weather cooperates. 

Then, on Saturday July 28, there was an outing to 

Peggy’s Cove, followed by dinner at the Sou’Wester restaurant 

there. Despite the fact that visibility was reduced to less 

than a kilometer by fog, the students seemed to enjoy the 

experience. To underline the cosmopolitan nature of the 

group, when a call was made by one of the students to sing 

happy birthday to the Brazilian student, on the ride home, 

birthday wishes were sung in English, Romanian, French, 

Spanish and Mandarin. This was a very successful event, 

and a fitting conclusion to Dalhousie’s term as host. The 

next School will be held in Fredericton, at the University of 

New Brunswick. 


AARMS Postdoctoral Fellowship Program 

In the 2007 competition, one Postdoctoral Fellowship was 

awarded to: Rebecca Hammond (Acadia University, supervised 

by Richard Karsten and Holger Teismann). The PDFs 

awarded in the previous year to Toby Kenney (Dalhousie 

University, supervised by Robert Pare and Richard Wood) 

and to Dansheng Yu (Saint Francis Xavier University, 

supervised by Zhou Ping) continued for a second year. 

AARMS Distinguished Lecture Series 

There was one AARMS Distinguished Lecturer in 2007: 

Neil Calkin (Clemson) 

Topics: 

• Tossing Coins, and a Random Shooting Game of Lampert 

and Slater 

• Recounting the Rationals 

• Clemson’s Research Experience for Undergraduates 

Lectures took place at Acadia, Dalhousie, Mount Allison, 

Saint Francis Xavier, Saint Mary’s Universities, and in the 

Coast to Coast Seminar Series. 

Scientific Activities 

The following conferences, workshops and scientific activities 

were funded or co-funded by AARMS in 2007: 

2nd AARMS/Dalhousie Atlantic Analysis Days 

Organizer: Karl Dilcher 

Dalhousie University, March 30-31, 2007 

East Coast Combinatorial Conference 2007 

Organizer: Catharine Baker 

Mount Allison University, April 18-19, 2007 

Workshop on Mathematical Knowledge Management 

Organizer: Jonathan Borwein 

Dalhousie University, April 26-28, 2007 

Black Holes VI 

Organizer: Jack Gegenberg 

White Point Beach Resort, Nova Scotia, May 12-16, 2007 

The Austin and Hempel Lecture: Some Recent Thoughts 

by Alasdair Urquhart, University of Toronto 

Dalhousie University, May 17, 2007 

12th Canadian Conference on General Relativity and 

Relativistic Astrophysics 

Organizer: Jack Gegenberg 

University of New Brunswick, Fredericton, May 17-20, 2007 

117


Canadian Mathematics Education Study Group (CMESG) 

Annual Meeting 

Organizer: John Grant McLoughlin 

University of New Brunswick, Fredericton, June 8-12, 2007 

Statistical Society of Canada Annual Meeting (SSC-2007) 

Special Session: Controversies over Fish Stocks 

Organizer: Noel Cadigan 

Memorial University, June 10-13, 2007 

Workshop on Noncommutative Geometry 

Organizer: Dan Kucerovsky 

University of New Brunswick, Fredericton, June 11-15, 2007 

AARMS/ACEnet/MITACS Summer Training Workshop 

in High Performance Computing in the Mathematical 

Sciences 

Organizer: Hugh Chipman, Richard Karsten, Ronald 

Haynes, Duane Currie 

Acadia University, July 9-14, 2007 

Bluenose Numerical Analysis Day 2007 

Organizers: Pat Keast, Paul Muir, Richard Karsten, 

Ronald Haynes 

Saint Mary’s University, July 27, 2007 

International Workshop on Groups, Rings, Lie and Hopf 

Algebras II 

Organizer: Yuri Bahturin 

Bonne Bay Marine Station, Memorial University, August 

13-17, 2007 

4th Workshop on Combinatorial and Algorithmic 

Aspects of Networking 

Organizer: Norbert Zeh 

Dalhousie University, August 14, 2007 

10th Workshop on Algorithms and Data Structures 

(WADS 2007) 

Organizer: Norbert Zeh 

Dalhousie University, August 15-17, 2007 

APICS Meeting: Special Sessions in Mathematics and 

Statistics 

Organizers: Colin Ingalls, Rolf Turner, Maureen Tingley 

University of New Brunswick, Fredericton, October, 12-13 

2007 

Dalhousie Euler Symposium 

Organizers: K. Dilcher, R. Smirnov, S. Swaminathan 

Dalhousie University, October, 26-27 2007 

118 

Relativity in Cape Breton: A General Relativity and Cosmology 

Workshop 

Organizer: Robert van den Hoogen 

Mabou River Inn, Mabou, Nova Scotia, October 26-28, 

2007 

Reports from the above activities are lodged online and can 

be read at http://www.aarms.math.ca/events/past.php 

AARMS Monograph Series 

The first volume in the AARMS Monograph Series, in collaboration 

with the AMS is in production and is expected 

in April 2008: A Course on the Web Graph, by Anthony 

Bonato 

We encourage lecturers at the AARMS Summer School to 

submit manuscripts based on their specialist courses. There 

are three other manuscripts in the pipeline. The editorial 

board consists of the following people: 

Jonathan Borwein (Dalhousie University) 

Robert Dawson (Saint Mary’s University) 

Ron Fitzgerald (Math Resources Inc) 

Dan Kucerovsky (University of New Brunswick) 

Richard Wood (Dalhousie University) 

David Langstroth (Dalhousie University) 

David Langstroth


The Institute’s Commercial and Industrial Mathematics 

Program (CIM), acts as a bridge between the mathematics 

community and businesses that benefit from research in 

the mathematical sciences. In this way, the CIM program 

seeks to communicate results in mathematics to the business 

community, and conversely, to create an awareness 

among mathematicians of the needs of that community. 

Program activities include seminars and workshops in 

mathematical areas of direct interest to industry, networking 

activities, and assisting mathematicians in connecting 

with industry or in initiating their own commercial 

ventures. Activities take place across a broad spectrum of 

areas, of which financial mathematics forms one important 

part. The program is coordinated by the Fields Institute’s 

Industrial Advisory Board. 

Fields Symposia on the Mathematics of Transportation 

January–May 2008 

Organizer: Nicholas Kevlahan (McMaster) 

On 23 January 2008 the Fields Institute hosted a lively 

and stimulating workshop on the mathematics of transportation 

planning and management. This was a truly 

interdisciplinary meeting of civil engineers, professional 

transportation planners and (of course!) mathematicians. 

John Howe (of Metrolinx, the newly created government 

agency responsible for transportation planning in the 

Greater Toronto Area and Hamilton) gave an informative 

overview of the transportation and urban planning 

challenges facing us over the next twenty years. This 

presentation made it clear that successful transportation 

planning must involve not just freeways and public 

transit, but all levels of planning and management from 

the microscale of individual residents to the macroscale 

of region wide integrated urban planning on a 20 year 

horizon. The workshop finished with Reinhard Illner’s 


(Victoria) Applied Mathematics Colloquium lecture “From 

Fokker-Planck type kinetic traffic models to stop-and-go 

waves in dense traffic.” which showed how mathematical 

modelling can help understand vehicle movement on freeways. 

The workshop showed that there are many (perhaps 

surprising) ways in which mathematicians can contribute 

to this enterprise. This inspired the Fields Institute to 

continue the discussion by sponsoring a series of monthly 

symposia, each focused on a particular transportation 

theme. February’s symposium featured a fascinating talk 

by Eric Miller on agent-based micro-scale transportation 

modelling. This approach models the daily transportation 

decisions of millions of individuals, and allows us 

to examine how they respond to incentives, disincentives 

and changes in transportation options (e.g. a new rapid 

transit line). The discussion included questions about how 

to validate the model against real data and how to provide 

sensitivity estimates and confidence intervals for the 

results. 

In March Yuriy Zinchenko described Nesterov’s theory 

of static equilibria in congested transportation networks. 

Zinchenko showed that the 1950s era Beckmann model (the 

standard approach) significantly under-predicts congestion 

compared with the more sophisticated Nesterov theory. In 

addition, the Nesterov approach converges more quickly 

and should be numerically efficient. Yuriy also showed 

a nice homemade video, which used springs and strings 

to illustrate Braess’s Paradox. Braess’s Paradox states that 

adding extra capacity to a network can end up slowing 

everyone down! Discussion after Yuriy’s talk centred on 

ways to compare the two approaches in the operational 

traffic models actually used by engineers to manage road 

networks. 

In April Pavlos Kanaroglou described the state of the art in 

integrated transportation and land use modelling. Pavlos 

started off by recalling Jane Jacob’s (author of “The death 

and life of great American Cities” and long-time Toronto 

resident) understanding of cities as organized complexity. 

His goal is to design computer models of these dynamic 

complex nonlinear systems. A crucial component of these 

models (which are a bit like the computer game SimCity) 

is the coupling of land use and transportation models. In 

current transportation planning, land use (e.g. population 

density) is taken as fixed, and the planner attempts 

119


to optimize the transportation network assuming nothing 

else changes. There is no allowance for the fact that an 

improved transport network influences people’s decisions 

on where to live and work. Pavlos then described his own 

model: IMULATE and a related model called CLIMATE-C 

(which takes into account climate change). He started 

by using a small town in Greece as a test case, and is now 

scaling up to the city of Hamilton. The main mathematical 

challenges of these models is that they do not really capture 

nonlinearities and abrupt changes: the model is just recalibrated 

to the new data. Another fundamental problem 

is that the coupled equations become very complicated and 

difficult to solve. It would be useful to analyze the sensitivity, 

stability and accuracy of these models, as is done for 

climate and weather models. Perhaps the methods of data 

assimilation used in weather prediction could allow these 

integrated land use models to be updated continuously with 

new data (rather than at fixed intervals every five or ten years). 

Finally, in May Matheus Grasselli led a discussion on “Market 

solutions to transportation problems.” This was a good 

way to end the series since, once we’ve found an optimal 

solution, we still have to figure out how to implement it! 

Finding appropriate financial incentives and disincentives 

can also help people to use the available transportation 

resources more efficiently. In fact, John Howe of Metrolinx 

pointed out at our first meeting that finding a politically 

acceptable way to price and pay for transportation is the 

biggest challenge they face. 

Matheus’s approach is to consider transportation as a 

service, and then design a market for it. A market should 

provide consumer options, have efficient pricing (i.e. 

price should reflect the true marginal cost) and be neutral 

(comparable goods are treated equally). Unfortunately, 

our current transportation network violates all of these 

principles! The main theme of Matheus’ talk was how to 

“internalize externalities”, i.e. to ensure that the perceived 

price equals the marginal cost. For example, currently 

drivers pay only 60% of the total cost of driving. The most 

amusing (and mathematical) example was a cap-and-trade 

system for road capacity. This would create a market in road 

capacity (similar to the highly successful cap-and-trade system 

for acid rain in US). Although it sounds extreme, such 

a system is actually being proposed for Austin, Texas. Just 

like other markets, mathematicians will have lots of scope 

for designing financial products and determining optimal 

pricing for the new transportation markets. 

These Symposia have looked at the problems of transportation 

and planning from the engineering, planning and 

120 

financial perspectives. However, each of these viewpoints 

relies heavily on mathematical analysis and modelling. 

By bringing mathematicians together with transportation 

experts the Fields Institute hopes to foster new collaborations 

and new thinking on a problem that is of prime 

importance for the environment and for our quality of life. 


Eric Miller (Toronto) 

Agent-based transportation modelling 

Yuriy Zinchenko (McMaster) 

Stable traffic equilibria: Properties and applications 

Pavlos S. Kanaroglou (McMaster) 

Integrated transportation and land use models (ITLUMs): 

The McMaster experience 

Matheus Grasselli (McMaster) 

Market-based solutions to transportation problems 

Nicholas Kevlahan 

Industrial Optimization Seminar 

October 2007–May 2008 

Organizing and Advisory Committee: Tamás Terlaky 

(McMaster), Natalia Alexandrov (NASA), Andrew R. Conn 

(IBM Watson), John E. Dennis (Rice), Stefan Karisch (Carmen 

Systems), János Pintér (Pintér Consulting), Henry 

Wolkowicz (Waterloo), Margaret H. Wright (NYU), David 

Zingg (Toronto) 

The inaugural meeting of the Fields Industrial Optimization 

Seminar took place on November 2, 2004. This 

year was the fourth year for the seminar series, which is 

supported by both MITACS and the Fields Institute. The 

seminar meets in the early evening of the first Tuesday 

of each month. Each meeting is comprised of two related 

lectures on a topic in optimization; typically, one speaker 

is a university-based researcher and the other is from the 

private or government sector. The series welcomes the 

participation of everyone in the academic or industrial 

community with an interest in optimization – theory or 

practice, expert or student. 

This year the seminar series continued its established tradition 

and brought together a wide range of researchers and 

practitioners from both Canada and the USA. Following 

the previous years’ well-received theme of “Optimization 

for Radiation Therapy,” the October seminar resumed the 

series with a closer look at various mathematical models 

for robust and large-scale planning methods for intensity

modulated radiation therapy (IMRT) and image-guided 

radiation therapy (IGRT) currently employed at the 

Princess Margaret Hospital in Toronto and the Center 

for Operations Research in Medicine and Health Care at 

Georgia Tech. Their robustness towards residual errors is 

a crucial factor in successful treatment planning and also 

depends on the effective image registration for accurate 

tumour location, which was further addressed in the 

March Seminar by researchers from McMaster and Philips 

Research North America. 

Optimization and finance was the theme of the November 

seminar which focused on the valuation of financial derivatives 

and financial planning using both deterministic and 

stochastic optimization methods. Researchers from Rutgers 

and Goldman Sachs discussed both risk and quantitative 

portfolio management highlighting modern optimization 

as one of the key elements which provides innovative and 

sophisticated tools for transferring the excess return ideas 

into new financial instruments and multi-period portfolios. 

The interplay between aerodynamic shape optimization 

and fluid mechanics was addressed during the two seminars 

in December and April. At the December meeting, 

participants learned about new advances that allowed 

moving from the design of aerospace vehicles in simplified 

steady flow environments to full aircraft configurations, 

as illustrated on the business jet concept by Desktop Aeronautics. 

In addition, researchers from McGill discussed 

the modeling of unsteady flows for the improved modeling 

and optimization of helicopter rotors and other turbomachinery 

blades. Building in existing knowledge in fluid 

mechanics, the subsequent April Seminar further included 

various aspects of thermodynamics with industrial applications 

for the optimization of advanced welding techniques 

in the automotive industry, which are also of relevance for 

environmental modeling in the context of weather prediction 

at Environment Canada. 

Sharing its focus on the environment, the May Seminar 

continued the theme of “Energy and Electricity Generation” 

from previous years and addressed the optimal design 

of portfolios for water rights, leases, and options in the 

Southwestern Unites States using simulation techniques 

and stochastic Monte Carlo models of rainfall developed at 

NC State. The power and importance of optimization in the 

oil and gas industry for exploration, development, drilling, 

and production has also been highlighted by EXXON where 

optimization serves as a steady and successful analysis and 

decision-support tool. 


The February Seminar focused on combinatorial optimization 

problems and their application in telecommunications. 

Researchers from Carleton presented new solutions 

algorithms for machine learning, statistics, computational 

biology, and digital video broadcasting, and their relevance 

for the telecommunications industry was further 

emphasized by AT&T Labs Research who described several 

current application areas as varied as planning and design 

of optical and wireless networks, telephone and traffic 

migration, routing, and restoration, network survivability, 

e-commerce, and search engine design. 

The 2007-2008 series concluded with the June Seminar 

further developing the well-established theme on “Optimization 

in the Airline Industry” through presentations 

by researchers from Michigan and American Airlines. The 

special focus this year was on airline planning including 

fleet assignment, schedule development and revenue 

management, as well as the effects of O&D networks and 

pricing on the fleet assignment process. In addition, the 

link between airline plans and operational robustness in 

view of delay propagation and recovering from disruptions 

was discussed, also reemphasizing some of the robustness 

aspects addressed for radiation therapy at the beginning of 

the series. 

As the founding organizer Tamás Terlaky has moved from 

McMaster to Lehigh University, starting in 2008-09, the 

seminar will henceforth be organized by Antoine Deza 

(McMaster) as Chair of the Organizing Committee, and 

co-organized by Miguel Anjos (Waterloo) and Joaquim 

Martins (Toronto). The Industrial Optimization Seminar 

resumes in October 2008. 


Eva K. Lee (Georgia Institute of Technology and Emory 

University) 

Robust optimization to accommodate effects of systematic 

treatment uncertainties 

Timothy Craig (Princess Margaret Hospital) 

Accuracy in radiation therapy: Current achievements, future 

solutions 

Andras Prekopa (Rutgers Center for Operations Research) 

Optimization methods in valuation of financial derivatives 

and financial planning 

Reha Tutuncu (Goldman Sachs) 

Optimization and quantitative portfolio management 

Peter Sturdza (Desktop Aeronautics, Palo Alto) 

Design optimization of a supersonic natural laminar flow 

business jet 

121


Sivakumaran Nadarajah (McGill) 

Pushing the limits of optimum shape design for unsteady flows 

John W. Chinneck (Carleton) 

The maximum feasible subsystem problem and applications 

Mauricio G. C. Resende (AT&T Labs Research) 

Some combinatorial optimization problems arising in telecommunications 

Jan Modersitzki (McMaster) 

Numerical methods for image registration 

Vladimir Pekar (Philips Research North America) 

Image registration in radiation therapy planning 

Bartosz Protas (McMaster) 

Adjoint-based optimization in fluid mechanics: Theory, computations 

and industrial applications 

Saroja Polavarapu (Environment Canada) 

Four-dimensional variational assimilation in the context of 

weather prediction 

C.T. Kelly (North Carolina State University) 

Optimal design of municipal water supply portfolios with 

implicit filtering 

Amr El-Bakry (EXXON) 

Optimization in the oil and gas industry: the models and the 

challenges 

Amy Cohn (Michigan) 

“Optimized” airline plans and operational realities 

Timothy Jacobs (American Airlines) 

Integrating O&D passenger effects into the airline scheduling 

process 

Alexander Engau 

Quantitative Finance Seminar 

June 2007 – May 2008 

Organizers: Ron Dembo (zerofootprint), Matheus Grasselli 

(McMaster), John Hull (Toronto), Tom Hurd (McMaster), 

Moshe Milevsky (York), and Dan Rosen (R2 Financial 

Technologies) 

This year’s seminar series was conducted on the background 

of a remarkable and unsettling year in which the 

sub-prime mortgage crisis developed into a contagion that 

continues to pound the world’s financial markets. It was a 

year when daily news from the markets permeated many 

of the talks, adding a feeling of urgency and immediacy 

not often found in research mathematics. While a certain 

122 

amount of blame for these events has been placed on the 

“quants” who created such products as collateralized debt 

obligations and asset backed securities, a thoughtful analysis 

supports the view that the crisis has made mathematical 

innovation more relevant than ever to the art of financial 

risk management. 

The opening meeting, featuring Martin Schweizer and 

David Li, exemplified the mix of theoretical and applied 

finance we aim to achieve in the series. Schweizer addressed 

the longstanding theoretical problem of jointly modelling 

the dynamics of the family of plain vanilla options based on 

a single underlier. After a broad review of what has already 

been done on this topic, he outlined an approach that 

focuses on a new concept he calls “local implied volatilities”. 

This quantity serves as a good parametrization of the 

state space of the model, and can be treated with extensions 

of the general theory of stochastic differential equations. As 

Schweizer admitted, much work remains to be done on this 

problem. David Li took a respite from his front-line work 

on the credit crisis to tell us some background to the subprime 

problem. In a nutshell, it seems there was a strong 

breakdown in lending standards, and the consequent poor 

quality mortgages were bundled by the investment banks 

and resold to unwitting investors around the globe. In 

other words, the blame for the crisis can be attributed to the 

usual human failings: greed, laziness and a lack of imagination. 

Li also offered a modelling approach to handle the 

mortgage backed securities at the heart of the crisis. 

November’s meeting continued the mix of theory and 

application. Michael Walker talked on the subject of CDO’s 

(collateralized debt obligations), the portfolio credit derivatives 

that have played a central role in the credit crisis. This 

now controversial asset class has a natural structure that 

appeals to mathematicians, but whose complexity has led to 

misunderstandings of their risky nature. His methods lead 

to easy-to-calibrate models for valuation of index CDOs 

and the various related derivative contracts such as leveraged 

super-senior tranches. Thaleia Zariphopoulou’s talk 

explored themes on optimal investment. She introduced 

a new concept, the forward performance process, that 

extends the traditional value function process of utility 

maximization. Many examples were given that showed how 

this concept generalizes the standard theory, while leading 

to interesting classes of solvable nonlinear pdes. 

Rama Cont and Jim Gatheral braved winter storms to fly 

from New York to speak at our February meeting. Cont’s 

talk focussed on the relatively liquid CDO contracts written 

on the reference CDX and ITraxx portfolios. His prob-

lem is to construct a stochastic process for the portfolio 

default losses that is compatible with the observed prices 

of CDO tranches. His proposed solution is expressed as 

the constrained minimizer of relative entropy and can be 

found using the principles of convex duality. The method 

applied to observed prices reveals strong evidence for the 

dependence of loss transition rates on the past number of 

defaults, that is, quantitative evidence for contagion effects 

in the risk-neutral default loss process. In his talk, Gatheral 

dealt with options on VIX (the volatility index associated 

to the SP500 index) and options on variance swaps. He 

argued that accurate pricing of these important volatility 

derivatives requires extending from one to two stochastic 

volatility factors, and gave the so-called double Heston and 

double log-normal models as examples. 

The March meeting featured Peter Cotton and Roger Lee. 

Cotton expressed the view that the current credit crisis is 

partly attributable to a poor understanding of default correlations 

as described by copulas, and this in turn is due 

to a lack of relevant observations. To counter this fact, he 

suggested some models of other physical phenomena that 

might be describable in terms of the normal copula, in 

particular ten pin bowling and the incidence of rainfall in 

different locations. He described the extent to which data 

for these phenomena can be fit with the normal copula. 

Lee investigated the use of traded vanilla options as instruments 

for hedging variance and volatility derivatives. His 

talk showed that combining a static portfolio of options 

with a dynamic portfolio on the underlier can lead to an 

effective hedge of such instruments, as well as strong upper 

and lower bounds on their price. 

Michael Gordy and Leif Andersen spoke at our closing 

meeting in April. Gordy’s talk, on the subject of portfolio 

risk measurement, investigated how Monte Carlo methods 

for portfolio Value-at-Risk generally involves two levels 

of simulation. The outer level, in the physical probability 

measure, essentially generates scenarios under which the 

profit-loss is computed. The inner level, a risk-neutral 

simulation, is needed to compute the market value of 

derivatives or other nonlinear instruments making up the 

portfolio. He showed that the computational effort can 

be surprisingly small, provided that the division of work 

between the two levels is optimized. Andersen’s talk, liberally 

sprinkled with empirical data from the US gas market, 

investigated low-dimensional Markov models for practical 

trading of gas futures and options. He aimed for a realistic 

(seasonal) correlation structure and for perfect replication 

of the strongly seasonal form of gas option volatilities. 


As the financial crisis continues to rage unabated through 

the summer of 2008, we anticipate that the 2008-09 Quantitative 

Finance Series will again mix theory and practice in 

an entertaining and thought-provoking manner. 


Martin Schweizer (ETH) 

Arbitrage-free joint models for assets and derivatives 

David X. Li (Barclays Capital) 

Dynamical competing risk model for home equity loan securities 

Michael Walker (Toronto) 

A calibratable dynamic model for CDO’s: Application to 

leveraged-super-senior tranche valuation 

Thaleia Zariphopoulou (Austin) 

Stochastic pdes in portfolio choice 

Rama Cont (Columbia) 

Calibration of portfolio credit risk models: solution of an 

inverse problem via intensity control 

Jim Gatheral (Merrill Lynch and Courant Institute) 

Developments in volatility derivatives pricing 

Peter Cotton (Julius Finance Corporation) 

Bowling alone. Do copula models wash out? 

Roger Lee (Chicago) 

Hedging options on realized variance 

Leif Andersen (Bank of America Securities) 

Markov modeling of seasonal commodities 

Michael Gordy (Federal Reserve Board) 

Nested simulation in portfolio risk measurement 

Tom Hurd 

How I Became a Quant: Financial Engineers Give a 

Personal View of their Careers in Quantitative Finance 

October 17, 2007 

The Fields Institute acted as a catalyst for the second year 

in succession in bringing together practitioners, academics, 

and students in quantitative finance. Over 160 students and 

industry representatives participated in the event, which 

was organized by the International Association of Financial 

Engineers (IAFE) and sponsored by the pricing analytics 

software company Numerix. 

Financial Engineering is the discipline dedicated to developing 

and implementing practical solutions to economic 

and financial problems that result from the social interac- 

123


tions of humans, rather than those that originate in physics, 

chemistry, or biology. Its applications include trading and 

financial markets, commercial and retail banking, commodities, 

portfolio management, insurance, environmental 

problems, corporate investment decisions, and project 

planning. The recent explosive growth in the area has led 

students of all levels in mathematics, physics, computer science, 

and engineering students to wonder whether a career 

or an advanced degree in quantitative finance is right for 

them. With the rapid increase in sophisticated quantitative 

and computational techniques employed in financial firms, 

there is an increasing demand for students with quantitative 

backgrounds to work in the financial industry and an 

increase in post-graduate programs covering these topics. 

How I Became a Quant is a forum designed to give a personal 

view of the world of quantitative finance from the 

point of view of professionals with varying specialties. The 

forums have been held in previous years in London, Boston, 

Chicago, and Berkeley. This year’s event in Toronto was 

moderated for a second year by John Hull, an IAFE Senior 

Fellow from the University of Toronto. The four panelists 

represented broad backgrounds and experience. Julio De 

Jesus, who holds a PhD in chemical engineering from the 

University of Toronto, is the Senior Vice-President in Risk 

at CIBC. Technology firms were represented by Gregg 

Berman, the Head of Risk Business at RiskMetrics, a risk 

management software and services firm (originally spunoff 

by JP Morgan), and Meng Lu, the Senior Vice-President 

of Financial Engineering at Numerix, a pricing analytics 

firm. The fourth member of the panel was Roger Stein, the 

Managing Director of Research and Analytics at Moody’s, 

and an influential industry quant in the area of credit risk. 

Our panelists shared their experiences, war stories, and 

views of opportunities in the industry for financial engineers. 

They expressed their views of current financial 

problems and the role that may be expected of financial 

engineers over the next decade. Interestingly, and perhaps 

not unexpectedly, the panel generally expressed the collective 

view that a quant career resembles more a stochastic 

process (with jumps), rather than a deterministic path. This 

year, many memorable words of wisdom came right from 

the heart, and included “let’s face it, I’m a nerd, what else 

can I do?” and “my wife didn’t want me to be a lawyer… 

so I became a quant.” Clearly, no one can say that quants 

are not sensitive people–or, at least, that they do not have a 

sense of humour. 

Dan Rosen 

124 

MICS Electronic Journal 

Editors-in-Chief: Alistair Fitt (Southhampton) and John 

Ockendon (Oxford) Managing Editor: Huaxiong Huang 

(York) 

Mathematics-in-Industry Case Studies (MICS), a new 

Fields electronic journal launched in January 2008, started 

accepting submissions in July 2007. MICS aims to meet the 

publication needs of the burgeoning community of mathematicians 

who work on problems that are important to 

industry. Its central theme is the stimulation of innovative 

mathematics by the modelling and analysis of such problems 

across the physical, biological and social sciences. 

The intensely collaborative nature of industrial mathematics 

will be reflected in the way MICS attracts and processes 

papers. The editors-in-chief are John Ockendon (Oxford) 

and Alistair Fitt (Southampton), two leading figures in the 

mathematics-in-industry community. The editorial board 

includes many experienced researchers who are regularly 

involved in industrial problem-solving around the world. 

This will enable them to proactively encourage rapid publication 

of appropriate case studies. MICS will also accept 

and publish unsolicited submissions and it is planned that 

strong alliances with relevant websites and newsletters will 

create natural channels for such submissions. 

Although MICS has been conceived as the result of the 

vibrant Canadian culture of mathematics-in-industry, it 

intends to publish contributions from around the world, 

highlighting the commonality of key methodologies and 

pinpointing areas where mathematical creativity will have 

the most impact. 

The idea of MICS started when Bradd Hart was the acting 

director of Fields and it was through the help of many 

people over the past several years, including Tom Salisbury 

(former deputy director of Fields), Juris Steprāns (current 

deputy director of Fields) Robert Miura (NJIT), Pam Cook 

(Delaware), Nilima Nigam (McGill), and most importantly 

through the support of Barbara Keyfitz, (current director 

of Fields), and the hard work of Fields staff (Alison Conway, 

Richard Michael and Laura Gass), that MICS has become a 

reality.

To facilitate rapid publication and support public knowledge 

dissemination, MICS is entirely electronic and the 

Open Journal System of the Public Knowledge Project is used 

to handle manuscript submission and online publication. 

The first paper appeared in June 2008 and it is expected 

that 5-10 papers will be published in the 2008 volume. 

Huaxiong Huang 

START-UP FIRMS FOSTERED By THE FIELDS 

INSTITUTE 

In 1999, Fields began a program to foster start-up companies 

that commercialize mathematical ideas and that can 

benefit from co-location at the Fields Institute. Companies 

are approved by the Fields Board on recommendation by 

the IAB. The goal of the program is to enable members of 

the Fields community to start business ventures by giving 

them access to the physical, intellectual and logistical 

resources of the Institute. In 2008, one of the first start-up 

companies in this program, Sigma Analysis and Management, 

graduated from the program and moved off-campus, 

attaining the designation of a “senior” firm. 

The Individual Finance and Insurance Decisions (IFID) 

Centre @ the Fields Institute 

Moshe Milevsky 

The IFID Centre is a non-profit corporation that is currently 

housed at the Fields Institute and is closely associated 

with the Schulich School of Business and the Department 

of Mathematics and Statistics at York University in Toronto. 

The IFID Centre was launched in the Winter of 2001 with 

broad objectives and a mandate to conduct and disseminate 

applied research in the field of financial risk management 

for individuals. The IFID Centre supports a wide network 


of researchers interested in the topic of consumer finance 

and personal insurance by sponsoring conferences, generating 

research reports and giving targeted seminars and 

keynote presentations to audiences in the U.S. and Canada. 

The IFID Centre’s operating revenues and sponsorship 

grants are contributed by corporations in the financial 

services sector who are interested in directing research 

attention towards this field of growing importance and 

influence. 

To date The IFID Centre has sponsored and organized 

four annual conferences, generated and published over 

twenty research reports, and worked with over 30 different 

financial services companies and organizations around the 

world. In addition to its academic influence and presence, 

the financial media and press now view The IFID Centre as 

an accessible source of research and unbiased information 

on insurance, investments and retirement income planning. 

The next series of public IFID Centre activities will take 

place in November 2008, with a two-day conference 

devoted to financial engineering and mathematical finance 

& insurance. It is partially funded by MITACS and will be 

taking place at the Fields Institute on November 9 th & 10 th 

(organizing committee: T. S. Salisbury, M. A. Milevsky, 

H. Huang, D. S. Promislow, K. Moore and S. Jaimungal). 

A continuation one-day conference will be taking place in 

Chicago on November 11 th at the University of Chicago 

Gleacher Center (organizing committee: M.A. Milevsky 

and P. Chen). It will be devoted to applied research in the 

area of financial engineering and retirement income products. 

The IFID Centre’s organizational structure consists of an 

Executive Director (currently M. A. Milevsky), a governing 

board of directors (currently T. S. Salisbury and D.S. Promislow), 

in-house support staff, as well as junior and senior 

research associates. 

125


QWeMA Group Inc. 

Stemming from the activities of the non-profit IFID Centre, 

QWeMA Group Inc. is privately owned and operated by 

a group of financial engineers, economic scientists and 

applied mathematicians. In addition to being housed at the 

Institute, QWeMA is also a Corporate Affiliate Member of 

Fields. 

The QWeMA Group – which is an abbreviation for Quantitative 

Wealth Management Analytics Group – develops 

intellectual property, software algorithms and product 

solutions in the fields of wealth management, investments 

and insurance. We specialize in the business of retirement 

income planning and have worked with some of largest 

financial services companies in the world. 

QWeMA has offices in Toronto and Memphis and services 

clients in North and South America as well as Europe and 

the Far East. 

R2 Financial Technologies Inc. 

126 

Dan Rosen 

R2 Financial Technologies was founded in 2006 and is 

incubated at the Fields Institute in Toronto. 

Our mission is to deliver actionable, content-driven 

valuation, risk and capital management solutions, which 

effectively integrate advanced quantitative methodologies, 

financial technology and data. We create business value for 

our clients by delivering superior analytical capabilities in a 

simple, practical and intuitive way. 

The company is founded on the principles of individual 

leadership and creativity, excellence, and proven experience. 

We believe in a cross-disciplinary approach to solving 

business problems, which emphasizes the communication 

of complex ideas with clarity, precision and efficiency. 

Our senior management team has a combined 50-year 

practice designing, delivering and implementing technology 

solutions which are used at most of the top financial 

institutions around the world. 

SIGMA Analysis and Management 

David Rudd 

Sigma Analysis & Management is a financial firm initially 

housed within and assisted by the Fields Institute. Currently, 

Sigma is located at the MaRS Institute at University 

Avenue and College Street. Sigma was founded by David 

Rudd and Luis Seco of the University of Toronto. For the 

first eighteen months, Sigma analyzed the performance 

of hedge funds, trading advisors, and other investment 

managers who try to provide superior investment returns. 

The object of the research was to construct portfolios of 

investments which can insulate investors from risk to the 

economy and provide superior, sustainable returns. “Investors 

and institutions such as pension funds are looking 

for alternatives to exposure to the economy and will want 

positive returns with investment profiles not dependent on 

economic growth.” Sigma is now applying those research 

principals as an asset allocator and money manager. Sigma’s 

detailed research has remained proprietary and it does not 

accept public financial support. Sigma has seven full-time 

staff including four senior mathematics researchers and is 

also an investment counselor.


Ontario Mathematics Education Forum 

September 2007–June 2008 

Education Forum Steering Committee Co-chairs: Miroslav 

Lovric (McMaster) and Juris Steprāns (Fields) 

Members: Stewart Craven (Science centre), Shirley Dalrymple 

(York Region District School Board), John Kezys 

(Mohawk College), Donna Kotsopolous (Wilfrid Laurier), 

Dragana Martinovic (Windsor), Joyce Mgombelo (Brock), 

Katie Northcott (Crescent High School), Chris Suurtamm 

(Ottawa) 

The Ontario Mathematics Education Forum meets at 

the Fields Institute monthly during the school year, for 

a total of eight meetings (2007/8 dates were: 15 September, 

20 October, 19 January, 23 February, 29 March, 

26 April, 31 May), from 10am-2pm. Attendance ranges 

from 20 to 45, and participants come regularly from as 

far as Ottawa, Kingston, Peterborough, London, and St. 

Catherines. Meetings are open to the public and anyone 

may attend without invitation. Agendas are discussed and 

defined at the meetings of the Forum’s Steering Committee; 

there was a total of five Steering Committee meetings in 

2007/8; the first was a teleconference at the beginning of 

September 2007 where the dates of the meetings were determined, 

as well as the agenda for the September meeting. 

The Forum brings together individuals from university and 

college mathematics departments, faculties of education, 

teachers and mathematics coordinators from school boards, 

textbook publishers, freelance consultants, government 

representatives as well as members of the public interested 

in mathematics education. 

The Forum serves as a lively venue for sharing ideas and 

initiatives, discussing current issues in mathematics education 

and beyond, forging partnerships for mathematics 

education research, planning activities for mathematics 

education conferences and presenting numerous outreach 

activities. 

No matter what activity, certain questions are more or less 

constantly present on the agenda, in one form or another. 

For instance: How do we improve teaching and learning 

of mathematics? How do we better prepare mathematics 

teachers? How do we stimulate interest in studying and 

teaching mathematics? How do we forge productive links 

among various stakeholders? 


The 2007/8 monthly meetings dealt with a wide variety of 

mathematics education issues, such as: 

• discussion of Ontario grade 12 mathematics curriculum, 

in particular the Calculus and Vectors course; discussion 

of Ontario grades 7-10 math curriculum 

• transition from high school to college/university mathematics 

• research in mathematics education in Ontario 

• textbooks and their role in teaching and learning math 

landscape 

• learning objects and teaching and learning using the 

internet 

• multicultural and multilingual classrooms, etc. 

In 2007/8, we witnessed an increase in attendance and 

active participation among graduate students (mostly in 

math education; there were few mathematics grad students 

as well), which we believe is quite a success. 

Among our guest speakers this year we mention: 

• Anthony Azzopardi, Ministry of Education, Toronto 

• Jim Stewart, Professor Emeritus, McMaster 

• Jean-Marie De Koninck, Laval 

• Robin Kay, UOIT 

• Christine Ellis, Hillfield Strathallan College, Hamilton 

• Irene McEvoy, Ministry of Education 

• Pat Rogers, Dean of Education, Windsor 

• Jerome Pruloux, Ottawa 

• Mamokgethi Setati, University of South Africa 

Each meeting starts with information about activities 

of various mathematics education groups/organizations 

OAME (Ontario Association for Mathematics Education), 

OMCA (Ontario Mathematics Coordinators Association), 

OCMA (Ontario Colleges Mathematics Association), 

CMESG (Canadian Math Education Forum) and others. 

Then, the theme of the meeting is announced, and the 

Steering Committee member in charge of organizing the 

theme introduces the activities that will follow. 

Meetings: 

A good amount of time in our 15 September 2007 meeting 

was devoted to discussion of issues related to the curriculum 

implementation in grades 7-10 in Ontario. Adequate 

preparation and teacher education themes dominated the 

contributions from a large number of participants. We also 

127


talked about the upcoming Canadian Mathematics Education 

Forum (Vancouver, 2009), and encouraged formation 

of groups that will be invited to present their work. Unlike 

many other conferences/meetings, it is expected that a significant 

amount of work be done prior to the beginning of 

the Forum. The meeting ended with a conversation about 

the actual and desired roles of the Forum, the Forum’s 

newsletter and web site. 

The theme of the 20 October 2007 meeting ‘Math Curriculum, 

Textbooks, Education,’ tied views, opinions, and 

research on the relation between curriculum and textbooks. 

The two guests presented the two sides: Anthony Azzopardi 

from the Ministry of Education, Toronto talked about some 

aspects of the final revised secondary mathematics curriculum 

and implementation, whereas Jim Stewart (Professor 

Emeritus, McMaster) presented his views on textbook writing 

and design and their influence on curriculum design 

and implementation. To start the day, Miroslav Lovric 

outlined many issues that emerge when one decides to write 

about mathematics, be it a popular math book or a math 

textbook. Canadian Math Education Forum was again on 

the agenda, with updates presented by Kathryn Stewart, 

Peter Taylor and Walter Whiteley. 

Learning objects and their impact on math education were 

discussed in our last meeting in 2007, on 24 November. The 

themes were: 

• Learning Objects for College Students [Dawn Mercer, 

Seneca College] 

• Read/Write Learning Objects [George Gadanidis, University 

of Western Ontario] 

• Brock Students Learning Mathematics by Designing 

Learning Objects [Chantal Buteau, Brock University] 

• Fantasy Fractions Learning Object: A collaborative Project 

Between École Nouvel Horizon Elementary School 

and Brock University [Kamel Fodil, Michèle-Elise Lacroix 

(Ecole Nouvel Horizon); Chantal Buteau, Sarah Camilleri, 

Joyce Mgombelo, Jill Couture (Brock University)] 

• Newton’s Mind Interdisciplinary Learning Object [Miroslav 

Lovric, McMaster University] 

The five presentations touched upon numerous issues 

related to teaching and learning using internet resources. 

For instance, the fourth presentation introduced a collaborative 

project (2006-07) with a grade 5 class (with teacher 

and school principal) in the design and implementation of 

computer math games. The general feeling is that we are 

still far from completely understanding the full impact of 

computer and information technology on teaching and 

learning mathematics. 

128 

The 19 January 2008 meeting was our so-called ‘Research 

Day.’ The five presentations generated lively discussions, for 

which the allotted meeting time of three hours did not suffice. 

Presenters and their topics: 

1. Daniel Ansari, Assistant Professor and Canada Research 

Chair (Tier II), Developmental Cognitive Neuroscience 

in the Department of Psychology, Western 

Developing a sense of number: evidence from brain and 

behaviour 

2. Indigo Esmonde, Assistant professor in Mathematics 

Education at OISE, Toronto 

What counts as mathematics? Stories from families and 

from popular media 

3. Joanne Lee, Assistant Professor of Developmental Psychology, 

Department of Psychology, Wilfrid Laurier 

Can adult mathematics-related input facilitate the acquisition 

of number concepts by young children? 

4. Lionel LaCroix, Lecturer, Department of Pre-Service 

Teacher Education, Brock 

Semiotic interplay of mathematics learning activity in an 

apprenticeship training classroom 

5. Catherine D. Bruce, Assistant Professor, School of Education, 

Trent 

Lesson study as a method of professional development for 

teachers using SmartBoards to enhance mathematics teaching 

and learning 

The theme of 23 February 2008 meeting related to the 

complex issues of multiculturalism and multilingualism 

in the classroom. Videoconference with researchers in 

South Africa focused on the following questions: What do 

multilingual mathematics classrooms look and sound like? 

What makes them multilingual? What does this mean for 

teaching? In the afternoon, there were two research presentations: 

• Richard Barwell, Ottawa 

Mathematics teaching and multilingual learners in a UK 

primary school: an example involving word problems 

• Mamokgethi Setati, University of South Africa 

Using language as a transparent resource in the teaching 

and learning of mathematics in a Grade 11 multilingual 

classroom 

Technology in teaching was on the agenda of the 29 March 

2008 meeting. A presentation on the use of a smartboard 

in a high school mathematics classroom started a long 

discussion on teaching mathematics using modern technology. 

Although technology has been on the agenda of many 

conferences, workshops and meetings, some fundamental 

issues are still far from resolved. Shirley Dalrymple

designed a sequence of PowerPoint slides to illustrate the 

use of clickers. Christine Ellis from Hillfield Strathallan 

College, Hamilton, presented her experiences. Robin Kay 

from UOIT concluded the discussion with his talk entitled 

Investigating the Use of Learning Objects in Secondary School 

Mathematics Classrooms. The afternoon time slot was 

devoted to the conversation about the role of media in promotion 

of mathematics, inspired by the lively presentation 

of Jean-Marie De Koninck. 

The 26 April 2008 meeting had two themes. The morning 

portion of the meeting was devoted to the discussion of 

issues in elementary and secondary teacher education. 

Research presentations by Donna Kotsopoulos and her 

students – future teachers (Laura Cash, Heather Cumine, 

Elisa Goldman, Yogna Koovarjee) generated lots of attention. 

Our guest Jerome Pruloux talked about mathematical 

education of secondary mathematics teachers. In her presentation, 

Pat Rogers (Windsor) described her experiences 

and observations from visiting Japanese elementary classrooms. 

The afternoon portion was devoted to the Vectors 

and Calculus course. The four participants 

• Irene McEvoy (Ministry of Education) 

• David Poole (Trent) 

• Liisa Suurtamm (DSB Niagara) 

• Greg Tessaro (Crescent School) 

presented their views on organization of the course, its 

content, and modes of delivery. 

The theme of the last meeting of the year, on 31 May 2008, was 

‘Generating Interest in Mathematics.’ In several presentations, 

issues of access, interest, gender, etc. were discussed: 

• Jennifer Hall (graduate student Ottawa) Gender issues in 

post-secondary mathematics enrollment and perseverance 

• Amanjot Toor (undergraduate student Brock) Gender differences 

at undergraduate level in mathematics and a brief 

look at mathematics technology 

• John Mighton Update on the successes of the JUMP program 

In the afternoon, Murat Tuncali and Doug Franks 

described the Nipissing University Math Fair and introduced 

the recent winners: 

• Tamara Schindeler, Pinewood Public School, Unusual 

Graphs to Display Numerical Information (Intermediate) – 

presented as poster 

• Jonathan Tot and Dominic Girogetti, Widdifield Secondary 

School, General Polynomial Theorem and Associated 

Combinatorics (Senior) – live presentation. 

Miroslav Lovric 

Outreach Programs and Workshops 


SNAP Mathematics Fair and Conference 

May 16, 2008 

Organizer: Tanya Thompson 

Over 50 educators from across Ontario attended the SNAP 

Math Fair this year. Since its inception 11 years ago, these 

events have ignited the mathematical minds of students 

through the use of classic puzzles and problems. Students 

solve these interesting problems and then build an interactive, 

hands-on project which includes a model to help the 

passers-by solve the problems. SNAP math fairs provide an 

opportunity for elementary school communities to gather 

together to celebrate mathematics! 

Tanya Thompson, a former teacher and currently the Director 

of Education Programs for ThinkFun, Inc. and a board 

member of SNAP, once again organized the conference and 

presented details about SNAP Math Fairs. Troy Comish, a 

Resource Teacher for the Simcoe County Board of Education, 

presented his observations about math fairs based on 

his own experiences in promoting them throughout his 

board. Ron Lancaster, an OISE lecturer, engaged the participants 

in the Candy Problem demonstrating how teachers 

can use puzzles to teach mathematics. Bonnie MacDonald 

and Anthony Meli, Toronto District School Board Instructional 

Leaders, shared their experiences and successes using 

Math Fairs as a Toronto District School Board pilot project. 

Bill Ritchie, the co-founder and CEO of ThinkFun, Inc. and 

a board member of SNAP, showed how using his company’s 

mind-challenging games can be used to teach problem solving. 

Tiina Hohn, a professor from Grant MacEwan College 

in Alberta and a board member of SNAP, talked of the history 

of SNAP Mathematics Foundation and also how cards 

can be used in the mathematics classroom. Jim Timourian, 

a professor emeritus at the University of Alberta and the 

Chair of the SNAP board, talked about the positive features 

and qualities of a SNAP math fair. 

The main highlight of the conference was a SNAP Math 

Fair presented by over forty K-8 students of the St. Catherine 

Catholic Elementary School in Peterborough. These 

students, under the guidance of their teacher Judith Rioux- 

Wilson, astounded the conference participants with their 

excitement and knowledge of their math fair projects. The 

participants were able to witness first-hand the many benefits 

to the students of taking part in a SNAP math fair. 

129


Many thanks are expressed to the sponsors of the conference 

– the SNAP Mathematics Foundation (www.mathfair. 

com), PIMS – The Pacific Institute for the Mathematical 

Sciences (www.pims.math.ca ) and Grant MacEwan College 

(www.macewan.ca). 

The SNAP Math Fairs conference at Fields was an outstanding 

success. Educators learned how to inspire their students 

through creative, interactive mathematical puzzles and 

problems. They saw how students took ownership of these 

age old puzzles and gained confidence in many areas of 

problem solving. Since the launch of SNAP Math Fairs in 

Ontario just over 3 years ago, many schools have begun 

participating in SNAP math fairs and this movement continues 

to grow stronger each year! 

Tanya Thompson 

Math Performance Festival 

The Math Performance Festival (available at www. mathfest.ca) 

is a project by George Gadanidis (Western), Susan 

Gerofsky (UBC) and Rick Jardine (Western). The Festival is 

sponsored by the Fields Institute, the Faculty of Education 

at UWO, and the Canadian Mathematical Society. 

The Festival invites students and teachers to share their 

mathematical performances (poems, songs, skits, and 

artwork) through the Festival’s website. We hope that the 

Festival will help make mathematics ideas more likely to be 

discussed outside of math classrooms and the community 

of mathematicians, just as one might with a favourite book 

or a good movie. 

What does a mathematical performance look like? Here are 

three examples. 

Now I’m a Trapezoid (available at www.edu.uwo.ca/mathscene/geometry/geo1.html) 

is a song by a triangle that lost 

her head. Saddened by this loss, the triangle laments that 

it’s now a trapezoid. A triangle loses it ‘head’ and becomes 

a trapezoid. 

Measuring the Millimetres to You (available at www.edu. 

uwo.ca/mathscene/pst/pst5.html) is a song written and 

performed by two UWO preservice teachers. In this romantic 

ballad, two friends are saddened because of the great 

distance (100,000 mm) that separates them. Then, they 

realize that 100,000 mm is the same as 10,000 cm. And, if 

they divide by 10 and by 10 again, they are really not that 

far apart: only 100 m. 

130 

Little Quad’s Quest (available at http://www.edu.uwo. 

ca/mathscene/lq/lq1.html) is a five-part shadow theatre 

performance created by a class of fifth-grade students. 

Little Quad (shaped like a kite) is in search of his identity. 

Unlike Little Quad, all of Little Quad’s quadrilateral friends 

(Square, Rectangle, Rhombus and Trapezoid), have their 

own special mathematical names. What is Little Quad’s 

math name? 

Performances submitted to the Festival are adjudicated 

by a group of mathematics educators and by the following 

celebrities: 

Susan Aglukark, singer, songwriter, 3-time Juno Award 

recipient, Officer of the Order of Canada award in 2005. 

Tracy Bone, singer, songwriter, “Best Female Artist” of the 

2007 Canadian Aboriginal Music Awards. 

Douglas Coupland, novelist, playwright, filmmaker and 

visual artist, author of the bestseller jPod.

Bob Hallett of Great Big Sea, latest album: Fortune’s Favour. 

Jay Ingram, award-winning co-host and producer of Daily- 

Planet (Discovery Channel). 

The Festival is open to all mathematics students and teachers/professors 

(Kindergarten to University) – so please 

share your math performance! 

George Gadanidis 

Windows into Elementary Mathematics 

Windows into Elementary Mathematics (www.fields. 

utoronto.ca/mathwindows) is a Fields Institute outreach 

project developed by George Gadanidis (Western). The 

Windows into Elementary Mathematics project invites 

prominent mathematicians to discuss topics from elementary 

mathematics. Each Window includes the following 

components: video clips, interactive content, activities, and 

a poster on the theme. 

One goal of the project is to provide students, parents and 

teachers with insights into the thinking of mathematicians. 

Another goal is to help the public better appreciate the 

beauty of mathematics and mathematical ideas. 

The posters that accompany the Windows are available in 

digital form on the project website and will also be available 

in print form. We are considering ways of displaying the 

posters in public places, like libraries, subways, and buses. 

So far we have developed three Windows. The first two 

Windows, by Ken Davidson (Waterloo), focus on mathematical 

proof. 

1. The Sum of Odd Numbers 

2. The Konigsberg Bridges Problem 

The third Window, by Megumi Harada (McMaster), 

explores spherical geometry. 

3. Do Parallel Lines Meet? 

The next Window will feature Lindi Wahl (Western) on the 

topic of growth patterns. 

In the videos, the mathematicians also talk about their 

views of mathematics. For example, Megumi Harada discusses 

that “I love mathematicians. I can say that without 

any doubt that the math students were the most fun to be 

around, and I think it’s because, as a group, mathematicians 

love what they do more than many, many other 

groups of people I know.” 

George Gadanidis 


JUMP TRAINING SEMINARS 2008 

JUMP Math (www.jumpmath.org) is a charitable organization 

working to create a numerate society. Founded 

by mathematician John Mighton in 1998 as a tutoring 

program for struggling students, JUMP initially operated in 

his apartment with seven tutors and fifteen students. Today, 

the JUMP Math program is primarily focused on classroom 

use by teachers, and its materials are in over 400 educational 

institutions across Canada as well as in the United 

Kingdom, the United States, and South Africa. 

Until December 2004, JUMP’s administrative office was at 

the Fields Institute. As JUMP Math grew it also relocated, 

and eight full-time staff now occupy its office in the 

Toronto Star Building at One Yonge Street, but Fields continues 

to supply space for JUMP’s local training seminars. 

JUMP Math is committed to educational equity for all 

students. JUMP – short for Junior Undiscovered Math 

Prodigies – builds math confidence and skills in both 

students and teachers, enabling students to overcome math 

anxiety and succeed in the subject. John Mighton, who is a 

Fellow of the Fields Institute, obtained his Ph.D. from the 

University of Toronto, where he is currently an Adjunct 

Professor. He is also the author of The Myth of Ability and 

The End of Ignorance and an award-winning playwright. 

He has received an Ashoka Fellowship as a social entrepreneur 

for his work in fostering numeracy and building 

young children’s self-confidence through JUMP Math. He 

continues to work with JUMP’s staff writers to produce new 

editions of the workbooks as well as teacher’s guides and 

other free online support materials. He also conducts the 

training seminars at Fields and in other cities around the 

country. 

These seminars are important for training participants, as 

well as other educators, in JUMP’s National Book Fund. 

Now in its second year of implementation, the Book Fund 

provides professional development, class sets of gradespecific 

workbooks, teachers’ guides, and other support to 

teachers in classrooms facing financial barriers and with 

students who demonstrate academic need. 

The training seminars and other parts of the JUMP 

program give educators the tools to help students excel in 

math. JUMP Math is very grateful for the Fields Institute’s 

continued support of its mission. 

Kevin Linder 

131


Math Circle 

Larry Rice and Rad de Peiza have many years experience 

teaching mathematics. Both are retired high school teachers 

with decades of practice under their belts. Yet Rice and de 

Peiza do something that sets them apart from their colleagues: 

each and every Saturday afternoon they volunteer 

their time and expertise to host math circles for high 

school students. Held at Fields, the math circles are interactive 

lecture sessions for students from across the greater 

Toronto area. Rice and de Peiza offer the students a chance 

to learn material from outside of their regular curriculum, 

providing new challenges to these bright and enthusiastic 

students. As de Peiza stated, “Those in attendance are 

among the most promising mathematics students in the 

greater Toronto area.” 

Anywhere from twenty to seventy students attend these 

free informal sessions which typically last about two hours. 

Students are not required to make a commitment, as Rice 

and de Peiza say, but are encouraged to attend out of enjoyment 

and enthusiasm. Grade twelve student Emily Hsu has 

attended almost every Saturday since September 2007: “The 

teachers are really funny and nice. I enjoy coming because 

I learn different ways of solving problems. I hadn’t been 

to anything like this before and I find it really interesting. 

I even brought a couple of friends from school.” Parents 

of the students are equally pleased. “I drive my son here 

from Mississauga each Saturday,” says one mother. “He 

really enjoys it and I am happy that Fields is offering this 

program.” 

Rice and de Peiza have been hosting Math Circles at various 

locations for many years and have been at Fields since September 

2007. The two alternate teaching using a lively and 

interactive approach. Their passion for mathematics education 

is evident: “We volunteer to run these sessions because 

we love it. It’s fun for us, and we enjoy helping these kids 

reach their potential.” Rice and de Peiza are pleased to host 

their program at Fields, giving the high school students a 

chance to learn in a university-like setting. By the end of 

the school year Rice and de Peiza hope to take the students 

to a full-day math competition at the University of Western 

Ontario to celebrate their progress. 

In 2008-2009 the math circles at Fields promise to be bigger 

and better. “With a $10,000 grant from Angoss Software 

Corporation we will be able to expand the program and get 

more students involved,” says Rice. “We’d like to be able to 

advertise in high schools across the city. We are very proud 

of our program and we hope to extend opportunities to 

many other students.” 

132 

Some of the students who have attended the math circles 

have already gone on to represent Canada at the International 

Mathematical Olympiad, the most elite and 

prestigious of mathematics competitions. 

Emily Baillie

Fields Institute Fellows 

The honour of being named a Fields Institute Fellow was 

established as a part of the Fields tenth anniversary celebration 

in 2002. It is a lifetime appointment for individuals 

who have made outstanding contributions to the Fields 

Institute and to the Canadian mathematical community. 

Listed below are the names of all Fields Fellows, with the 

2008 recipients in bold. 

JaMeS G. aRThuR University of Toronto 

eDwaRD BieRSTone University of Toronto 

AllAn borodIn University of Toronto 

DaViD BoyD University of British Columbia 

DaViD R. BRillinGeR University of California–Berkeley 

heRMann BRunneR Memorial University of Newfoundland 

aRThuR CaRTy National Science Advisor, Government of 

Canada 

John ChaDaM University of Pittsburgh 

JennIfer chAyes Microsoft 

STephen a. CooK University of Toronto 

DeReK CoRneil University of Toronto 

h.S.M. CoxeTeR* University of Toronto 

walTeR CRaiG McMaster University 

DonalD DawSon Carleton University and McGill University 

KenneTh R. DaViDSon University of Waterloo 

Ron DeMBo Zerofootprint 

GeoRGe ellioTT University of Toronto 

Joel FelDMan University of British Columbia 

peTeR FillMoRe Dalhousie University 

John B. FRieDlanDeR University of Toronto 

GeoRGe GaDaniDiS University of Western Ontario 

alan GeoRGe University of Waterloo 

MaRK GoReSKy Institute for Advanced Study 

STephen halpeRin University of Maryland 

Gila hanna OISE–University of Toronto 

BRaDD haRT McMaster University 

huaxionG huanG York University 

rIcK JArdIne University of Western Ontario 

liSa JeFFRey University of Toronto 

VauGhan JoneS University of California–Berkeley 

RiChaRD Kane University of Western Ontario 

ManFReD KolSTeR McMaster University 

FRançoiS lalonDe Université de Montreal 

peTeR lanCaSTeR University of Calgary 

williaM lanGFoRD University of Guelph 

anna lawniCzaK University of Guelph 

Fields Institute Fellows 

Angus MAcIntyre University of Oxford 

JeRRolD e. MaRSDen California Institute of Technology 

John MCKay Concordia University 

John MiGhTon JUMP 

MoShe a. MileVSKy IFID Centre and Schulich School of 

Business 

RoBeRT V. MooDy University of Alberta 

eRiC MulleR Brock University 

RaM MuRTy Queen’s University 

V. KuMaR MuRTy University of Toronto 

peTeR J. niCholSon OECD–Paris 

GeoRGe o’BRien York University 

aMiT oza Princess Margeret Hospital 

JoSeF palDuS University of Waterloo 

eDwin peRKinS University of British Columbia 

niCholaS pippenGeR Princeton University 

williaM R. pulleyBlanK IBM Thomas J. Watson Research 

Centre 

nanCy ReiD University of Toronto 

CaRl RiehM McMaster University 

DaViD RuDD Sigma Analysis and Management 

ThoMaS SaliSBuRy York University 

luiS a. SeCo University of Toronto 

williaM F. ShaDwiCK Finance Development Centre, London 

MiChael SiGal University of Toronto 

ClauDine SiMSon LSI Corporation 

SiV SiValoGanaThan University of Waterloo 

ViCToR SnaiTh University of Southampton 

JuRiS STepRānS York University 

cAMeron stewArt University of Waterloo 

JaMeS STewaRT McMaster University 

TaMáS TeRlaKy McMaster University 

niCole ToMCzaK-JaeGeRMann University of Alberta 

KAren uhlenbecK University of Texas 

noRiKo yui Queen’s University 

*deceased 

133

Publications 

Fields Institute Publications 

Fields Institute Monographs Series 

The Fields Institute Monographs Series (Series Code: FIM) 

features high-quality research monographs growing out of 

various activities at the Fields Institute, including graduate 

course lectures and seminars. All Monographs are available 

for purchase from the American Mathematical Society 

Online Bookstore. The Institute also has a limited number 

available at our front desk. 

Listed by volume number 

1 Global Dynamics, Phase Space Transport, Orbits 

Homoclinic to Resonances, and Applications, by Stephen 

Wiggins, California Institute of Technology, AMS, 1993, 

155pp. 

2 Galois Module Structure, by Victor Snaith, McMaster 

University, AMS, 1994, 207pp. 

3 Lectures on Operator Theory and Its Applications, ed. P. 

Lancaster, University of Calgary, AMS, 1996, 339pp. 

4 Riemannian Geometry, eds. M. Lovric, M. Min-Oo and 

Y-K Wang, McMaster University, AMS, 1996, 115pp. 

5 Multiplicative Galois Module Structure, by A. Weiss, 

University of Alberta, AMS, 1996, 95pp. 

6 C*-Algebras by Example, by K. R. Davidson, University 

of Waterloo, AMS, 1996, 309pp. 

7 Bordism, Stable Homotopy and Adams Spectral 

Sequences, by S. O. Kochman, York University, AMS, 

1996, 272pp. 

8 Lifting Solutions to Perturbing Problems in C*-algebras, 

by T. Loring, University of New Mexico, AMS, 1997, 

165pp. 

9 Introduction to Homotopy Theory, by P. Selick, University 

of Toronto, AMS, 1997, 188pp. 

10 Quasi-Crystals and Discrete Geometry, ed. by J. Patera, 

University of Montreal, AMS, 1998, 289pp. 

11 Shape, Smoothness and Invariant Stratification of an 

Attracting Set for Delayed Monotone Positive Feedback, 

by Tibor Krisztin, University of Szeged, Bolyai Institute, 

Hans-Otto Walther, Universität Giessen, and Jianhong 

Wu, York University, AMS, 1999, 256pp. 

12 Ordered Exponential Fields, by S. Kuhlmann, University 

of Saskatchewan, AMS, 2000, 166pp. 

13 Lectures on Operator Theory, eds. R. Bhat, Indian Statistical 

Institute , G. A. Elliott University of Toronto, and 

P.A. Fillmore Dalhousie University, AMS, 1999, 323pp. 

14 Large Deviations, by F. den Hollander, Mathematical 

Institute, Nijmegen University , AMS, 2000, 143pp. 

134 

15 Lectures on Algebraic Model Theory, eds. B. Hart, M. 

Valeriote , McMaster University, AMS 2002, 111pp. 

16 Lectures on Monte Carlo Methods, by N. Madras, York 

University, AMS 2002, 103pp. 

17 Coloring of Mixed Hypergraphs: Theory, Algorithms and 

Applications, by V. I. Voloshin, Institute of Mathematics 

and Informatics of Moldavian Academy of Sciences, 

AMS 2002, 181pp. 

18 Meromorphic Functions and Linear Algebra, by O. 

Nevanlinna, Helsinki University of Technology, AMS 

2003, 136pp. 

19 Efficient Graph Representations, by J. Spinrad, Vanderbilt 


20 Lectures on Automorphic L-functions, by J.W. Cogdell, 

Oklahoma State University, H. H. Kim, University of 

Toronto, and R. Ram Murty, Queen’s University, AMS 

2004, 283pp. 

21 Introduction to Brauer Type Embedding Problems, by A. 

Ledet, Texas Tech. University, AMS 2005, 171pp. 

22 Modular Calabi-Yau Threefolds by Christian Meyer, 

Johannes Gutenberg University, AMS 2005, 194 pp. 

23 Coxeter Groups and Hopf Algebras, by Marcelo Aguiar, 

Texas A&M University, and Swapneel Mahajan, Indian 

Institute of Technology, AMS 2006, 181pp. 

24 Conformal Field Theory with Gauge Symmetry by Kenji 

Ueno, Kyoto University, AMS 2008, 168 pp. 

In preparation for the Fields Institute Monograph Series: 

• GANITA Seminars – Algebraic Curves in Cryptography, by 

K. Murty, University of Toronto. 

• Polyhedral and Semidefinite Programming Methods in 

Combinatorial Optimization, by L. Tuncel, University of 

Waterloo 

• Fields Institute Lecture Notes in Function Theory: Interpolation 

and Corona Problems, by Eric T. Sawyer, McMaster 


• Introduction to Mathematical Onocology, by S. Sivaloganathan, 

University of Waterloo. 

• Introduction to Orthogonal, Symplectic and Unitary Representations 

of Finite Groups, by C. Riehm, Fields Institute. 

• The classification of purely infinite C*-algebras using Kasparov’s 

theory, by E. Kirchberg, Humboldt-Universität zu 

Berlin 

• Lectures on Representations of Reductive Algebraic Groups, 

by C. Cunningham, University of Calgary and M. Nevins, 

University of Ottawa 

• Free Probability and Random Matrices, by J. Mingo and R. 

Speicher, Queen’s University. 

• Abelian Varieties and Cryptography, by K. Murty, University 

of Toronto

Fields Institute Communications Series 

The Fields Institute Communications Series features 

proceedings and lecture notes growing out of the various 

activities at The Fields Institute for Research in Mathematical 

Sciences. Many of the publications evolve from each 

year’s main program. Interdisciplinary titles also emerge 

from programs and workshops focusing on applications 

of mathematics in science, engineering, industry, and 

business. All Communications volumes are available for 

purchase from the American Mathematical Society Online 

Bookstore. The Institute also has a limited number available 

at our front desk. 

Listed by volume number 

1 Dynamics and Control of Mechanical Systems: The Falling 

Cat and Related Problems, ed. Michael J. Enos, The 

Fields Institute, AMS, 1993, 280pp. 

2 Control of Flexible Structures, ed. Kirsten Morris, University 

of Waterloo, AMS, 1993, 243pp. 

3 Hamiltonian and Gradient Flows, Algorithms, and Control, 

ed. Anthony Bloch, Ohio State University, AMS, 

1994, 155pp. 

4 Normal Forms and Homoclinic Chaos, eds. W. F. Langford, 

University of Guelph and W. Nagata, University of 

British Columbia, AMS, 1995, 294pp. 

5 Pattern Formation: Symmetry Methods and Applications, 

eds. J. Chadam, McMaster University; M. Golubitsky, 

University of Houston; W. Langford, University of 

Guelph and B. Wetton, University of British Columbia, 

AMS, 1996, 358pp. 

6 Pattern Formation and Lattice Gas Automata, eds. A. T. 

Lawniczak, University of Guelph/Univeristy of Toronto 

and R. Kapral, University of Toronto, AMS, 1996, 

346pp. 

7 Mechanics Day, eds. W. F. Shadwick, The Fields Institute; 

P.S. Krishnaprasad, University of Maryland and T. 

S. Ratiu, University of California at Santa Cruz, AMS, 

1996, 260pp. 

8 Conservative Systems and Quantum Chaos, eds. L. M. 

Bates and D. L. Rod, University of Calgary, AMS, 1996, 

176pp. 

9 Nonlinear Dynamics and Stochastic Mechanics, eds. W. 

H. Kliemann, Iowa State University; W. F. Langford, 

University of Guelph and N. Sri Namachchivaya, University 

of Illinois at Urbana-Champaign, AMS, 1996, 

238pp. 

10 Integration Algorithms for Classical Mechanics, ed. J. 

Marsden, California Institute of Technology; G. Patrick, 

University of Alberta and W. F. Shadwick, The Fields 

Publications 

Institute, AMS, 1996, 244pp. 

11 Nonlinear Dynamics and Time Series: A Bridge Between 

the Physical and Statistical Sciences, eds. C. Cutler, University 

of Waterloo and D. Kaplan, McGill University, 

AMS, 1996, 252pp. 

12 Free Probability Theory, ed. D. Voiculescu, University of 

California, Berkeley, AMS, 1997, 312pp. 

13 Operator Algebras and their Applications, eds. P. Fillmore, 

Dalhousie University and J. Mingo, Queen’s 


14 Special Functions, q-Series and Related Topics, eds. M. 

Ismail, University of South Florida; D. Masson, University 

of Toronto and M. Rahman, Carleton University, 

AMS, 1997, 277 pp. 

15 Sixth Canadian Conference on General Relativity and 

Relativistic Astrophysics , eds. S. Braham, Simon Fraser 

University, and J. Gegenberg and R. McKellar, UNB 

Fredericton, AMS, 1997, 373 pp. 

16 Algebraic K-Theory, ed. V. Snaith, McMaster University, 

AMS, 1997, 358 pp. 

17 Cyclic Cohomology and Noncommutative Geometry, eds. 

J. Cuntz, Heidelberg University and M. Khalkhali, University 

of Western Ontario, AMS, 1997, 189 pp. 

18 Topics in Semidefinite and Interior-Point Methods, eds. P. 

Pardalos, University of South Florida and H. Wolkowicz, 

University of Waterloo, AMS, 1998, 250pp. 

19 Stable and Unstable Homotopy, eds. William G. Dwyer, 

University of Notre Dame, Steve Halperin, University 

of Toronto, Richard Kane, University of Western 

Ontario, Stanley O. Kochman, York University, Mark 

E. Mahowld, Northwestern University, and Paul Selick, 

University of Toronto, AMS, 1998, 316pp. 

20 Operator Algebras and their Applications, Volume II, 

eds. Peter Fillmore, Dalhousie University and J. Mingo, 

Queen’s University, AMS, 1998, 170pp. 

21 Differential Equations with Applications to Biology, 

eds. S. Ruan, Dalhousie University, G.S.K. Wolkowicz, 

McMaster University and J. Wu, York University, AMS, 

1999, 509pp. 

22 Topology and Markets, ed. G. Chichilnisky, Columbia 


23 Topics in Game Theory and Mathematical Economics. 

Essays in Honor of Robert J. Aumann., ed. M. Wooders, 

University of Toronto, AMS, 1999, 291pp. 

24 The Arnoldfest. Proceedings of a Conference in Honour of 

V. I. Arnold for his Sixtieth Birthday., eds. E. Bierstone, 

B. Khesin, A. Khovanskii, University of Toronto, and J. 

E. Marsden, California Institute of Technology, AMS, 

1999, 555pp. 

135

Publications 

25 Operator Theory and Its Applications, eds. A. G. Ramm, 

Kansas State University, P. N. Shivakumar, University of 

Manitoba, and A. V. Strauss, Ulyanovsk State Pedagogical 


26 Monte Carlo Methods, ed. N. Madras, York University. 

AMS, 2000, 228pp. 

27 Hydrodynamic Limits and Related Topics, eds. S. Feng, 

McMaster University, A. T. Lawniczak, University of 

Guelph, S. R. S. Varadhan, Courant Institute of Mathematical 

Sciences – New York University, AMS, 2000, 

141pp. 

28 Analysis of Communication Networks: Call Centres, Traffic 

and Performance, eds. D. R. McDonald, University of 

Ottawa, and S. R. E. Turner, University of Cambridge, 

AMS, 2000, 200pp. 

29 Topics in Functional Differential and Difference Equations, 

eds. T. Faria, Universidade de Lisboa, and P. 

Freitas, Instituto Superior Técnico, AMS, 2001, 378pp. 

30 Mathematical Physics in Mathematics and Physics, ed. R. 

Longo, Dipartmento di Matematica Universita di Roma 

II, AMS, 2002, 451pp. 

31 Differential Equations and Dynamical Systems, eds. A. 

Galves, Universidade e Sao Paulo, J.K. Hale, Georgia 

Institute of Technology and C. Rocha, Instituto Superior 

Tecnico, AMS, 2002, 353pp. 

32 Valuation Theory and Its Applications Volume I, eds., 

F-V. Kuhlmann, S. Kuhlmann, M. Marshall, University 


33 Valuation Theory and Its Applications Volume II, eds., 

F-V. Kuhlmann, S. Kuhlmann, M. Marshall, University 


34 Numerical Methods and Stochastics, eds., T.J. Lyons, University 

of Oxford, and T.S. Salisbury, York University, 

AMS, 2002, 121pp. 

35 Symplectic and Contact Topology, eds., Y. Eliashberg, 

Stanford University, B. Khesin, University of Toronto, 

and F. Lalonde, UQAM, AMS, 2003, 199pp. 

36 Dynamical Systems and Their Applications to Biology, 

eds., S. Ruan, Dalhousie University, J. Wu, York University, 

and G.S.K. Wolkowicz, McMaster University, AMS, 

2003, 268pp. 

37 Novel Approaches to Hard Discrete Optimization, eds., 

P. Pardalos, University of Florida, and H. Wolkowicz, 

University of Waterloo, AMS, 2003, 181pp. 

38 Calabi-Yau Varieties and Mirror Symmetry, eds., N. 

Yui, Queen’s University and J.D. Lewis, University of 

Alberta, AMS 2003, 367pp. 

136 

39 Vertex Operator Algebras in Mathematics and Physics, 

eds., S. Berman, University of Saskatchewan, Y. Billig, 

Carleton University, Y.Z. Huang, Rutgers University, 

and J. Lepowsky, Rutgers University, AMS 2003, 249pp. 

40 Representations of Finite Dimensional Algebras and 

Related Topics in Lie Theory and Geometry, eds., V. 

Dlab, Carleton University and C. M. Ringel, Universität 

Bielefeld, AMS 2004, 479pp. 

41 High Primes and Misdemeanours: Lectures in Honour 

of the 60th Birthday of Hugh Cowie Williams, eds., A.J. 

van der Poorten, Macquarie University, and A. Stein, 

University of Illinois, Urbana, AMS 2004, 392pp 

42 Difference and Differential Equations, eds., S. Elaydi, 

Trinity University, G. Ladas, University of Rhode Island, 

J. Wu, York University, and X. Zou, Memorial University, 

AMS 2004, 438pp. 

43 Galois Theory, Hopf Algebras and Semiabelian Categories, 

eds., G. Janelidze, Georgian Academy of Sciences, B. 

Pareigis, University of Munich, and W. Tholen, York 


44 Asymptotic Methods in Stochastics: Festschrift for Miklós 

Csörgö, eds., L. Horvath, University of Utah, and B. 

Szyszkowicz, Carleton University, AMS 2004, 530pp. 

45 Representations of Algebras and Related Topics, eds., R-O. 

Buchweitz, University of Toronto, and H. Lenzing, University 

of Paderborn, AMS 2005, 396pp. 

46 Topics in Kinetic Theory, eds. Thierry Passot, CNRS, 

Catherine Sulem, University of Toronto, and Pierre-Louis 

Sulem, Observatoire de la Cote d’Azur, AMS 2005, 312 

pp. 

47 Geometry and Topology of Manifolds, eds., Hans U. 

Boden, Ian Hambleton, and Andrew J. Nicas, McMaster 

University, and B. Doug Park, University of Waterloo, 

AMS 2005, 347 pp. 

48 Nonlinear Dynamics and Evolution Equations, eds. 

Hermann Brunner and Xiao-Qiang Zhao, Memorial 

University of Newfoundland, and Xingfu Zou, University 

of Western Ontario, AMS 2006, 311 pp. 

49 Bifurcation Theory and Spatio-Temporal Pattern Formation, 

Wayne Nagata, University of British Columbia and 

N. Sri Namachchivaya, University of Illinois, Urbana- 

Champaign, AMS 2006, 177 pp. 

50 Universality and Renormalization: From Stochastic 

Evolution to Renormalization of Quantum Fields, eds. Ilia 

Binder, University of Toronto and Dirk Kreimer, Institut 

des Hautes Etudes Scientifiques, AMS 2007, 404 pp. 

51 Partially Hyperbolic Dynamics, Laminations, and Teichmüller 

Flow, eds. Giovanni Forni, University of Toronto, 

Mikhail Lyubich, SUNY at Stony Brook, Charles Pugh

and Michael Shub, University of Toronto, AMS 2007, 

339 pp. 

52 Pseudo-Differential Operators: Partial Differential Equations 

and Time-Frequency Analysis, eds. Luigi Rodino, 

Universita di Torino, Bert-Wolfgang Schulze, Universität 

Postdam and M.W. Wong, York University, AMS 

2007, 414 pp. 

53 Holomorphic Dynamics and Renormalization: A Volume 

in Honour of John Milnor’s 75th Birthday, eds. Mikhail 

Lyubich, University of Toronto and SUNY at Stony 

Brook and Michael Yampolsky, University of Toronto, 

AMS 2008, 395 pp. 

54 Modular Forms and String Duality, eds. Noriko Yui, 

Queen’s University, Helena Verrill, Louisiana State University 

and Charles F. Doran, University of Washington, 

AMS 2008, 297 pp. 

Forthcoming in the Fields Institute Communications 

Series: 

• Infinite Dimensional Dynamical Systems, ed. J. Mallet- 

Paret, Brown University, J. Wu, York University, Yingfei 

Yi, Georgia Institute of Technology, and Huaiping Zhu, 

York University. 

• Motives and Algebraic Cycles: A Conference Dedicated to 

the Mathematical Heritage of Spencer J. Bloch, ed. Rob 

de Jeu, Durham University, and J. Lewis, University of 

Alberta. 

• Taylor Model Methods, ed. M.Berz, Michigan State University, 

and K. Jackson, University of Toronto. 

• Global Optimization, ed. T. Coleman, University of 

Waterloo, and P. Pardalos, University of Florida. 

• A Survey of Mathematical Biology, ed. S. Sivaloganathan 

Co-publication with the AMS 

• The Coxeter Legacy: Reflections and Projections, ed., Ch. 

Davis and E.W. Ellers (University of Toronto), AMS 2006, 

320 pp. 

Fields Institute Publications Editorial Board Members 

Carl R. Riehm (Managing Editor) 

Barbara Lee Keyfitz (Director) 

Juris Steprāns (Deputy Director) 

James Arthur (Toronto) 

Kenneth R. Davidson (Waterloo) 

Lisa R. Jeffrey (Toronto) 

Tom Salisbury (York) 

Noriko Yui (Queen’s) 

Publications Manager: Debbie Iscoe 

Fields Notes 

Managing Editor: Emily Baillie 

Scientific Editor: Carl Riehm 

Publications 

The Fields Institute publishes a newsletter three times a 

year, titled Fields Notes. Issues appeared in September 2007, 

January 2008, and May 2008. Over 3500 copies of each issue 

are distributed free of charge in mailings to a wide range of 

universities throughout Canada, the United States, Europe, 

Asia, Australia and elsewhere. 

137

Governance 

Fields Institute Staff 

BaRBaRa lee KeyFiTz Director 

JuRiS STepRānS Deputy Director 

Directorate 

luKe ChanG Manager of Operations 

eMily Baillie Communications Officer 

Tanya neBeSna Administrative Coordinator 

JoSephine KaVanaGh Receptionist 

Program Team 

aliSon Conway Manager of Scientific Programs 

JaSon wu/VaneSSa GaRCia Thematic Program Coordinator 

JuDiTh Munn Scientific Program Coordinator 

ShaRon MCCalla Members Liaison 

Accounting 

uMa GupTa Financial Controller 

SaBRina SouSa/JaSon wu Accounting Assistant 

Computing 

philip SpenCeR Director of Computing Services 

Jon alexanDeR Computing Support Specialist 

Publications 

CaRl RiehM Managing Editor for Publications 

DeBBie iSCoe Publications Manager 

138 

Board of Directors 2007–2008 

Chair 

John R. GaRDneR Fields Institute 

Deputy Chair 

philip SilleR Eastport Capital Corp. 

BaRBaRa lee KeyFiTz Director, Fields Institute, Houston 

University 

JuRiS STepRānS Deputy Director, York University 

ian ainSwoRTh Mackenzie Financial 

MayeR alVo University of Ottawa 

John ChalliS University of Toronto 

ToM ColeMan University of Waterloo 

paTRiCK M. FiTzpaTRiCK University of Maryland 

JaneT e. halliwell JEH Associates Inc. 

FeRiDun haMDullahpuR Carleton University 


TRiSTRaM leTT Integra Capital Management 

philip SCoTT University of Ottawa 

JaniCe STein University of Toronto 

haRi VenKaTaChaRya CEO ZapIt Games 

STephen waTT University of Western Ontario 

eD wiTTen Institute for Advanced Study

Members of the Corporation 2007–2008 

Principal Sponsoring University Members 

FeRiDun haMDullahpuR Carleton University 

MaTThiaS neuFanG Carleton University 

BenJaMin STeinBeRG Carleton University 

John Capone McMaster University 


MaTThew ValeRioTe McMaster University 

MayeR alVo University of Ottawa 

philip SCoTT University of Ottawa 

VlaDiMiR peSToV University of Ottawa 

John BlanD University of Toronto 

John ChalliS University of Toronto 

SaFwaT G. zaKy University of Toronto 

ThoMaS ColeMan University of Waterloo 

RiChaRD CooK University of Waterloo 

SiV SiValoGanaThan University of Waterloo 

RiCK JaRDine University of Western Ontario 

DaViD JeFFRey University of Western Ontario 

STephen waTT University of Western Ontario 

CinDy Fu York University 

DonG lianG York University 

eRiC RuppeRT York University 

Directorate Members 

BaRBaRa lee KeyFiTz The Fields Institute 

KenneTh R. DaViDSon University of Waterloo 

JuRiS STepRānS The Fields Institute 

Corporate Affiliate Members 

alex KReinin Algorithmics Inc. 

DaViD FielD GM 

MoShe MileVSKy QWeMA Group Inc. 

Dan RoSen R2 Financial Technologies Inc. 

DaViD RuDD Sigma Analysis and Management 

Affiliate University Members 

MuRaT TunCali Nipissing University 

RoBeRT eRDahl Queen’s University 

GoRDon SiMonS Royal Military College 

ReeM yawaSSi Trent University 

anna lawniCzaK University of Guelph 

MaTThew niCol University of Houston 

aBBa GuMel University of Manitoba 

Governance 

paTRiCK M. FiTzpaTRiCK University of Maryland 

ChRiSTine SoTeRoS University of Saskatchewan 

S. eJaz ahMeD University of Windsor 

GReG lewiS University of Ontario Institute of Technology 

SyD BulMan-FleMinG Wilfrid Laurier University 

Members at Large 

ian ainSwoRTh Mackenzie Financial Inc. 

RiChaRD BonD University of Toronto, CITA 

John CRow Lawrence and Company Inc. 


John R. GaRDneR The Fields Institute 

peTeR GoDSoe AIMS 

John GuCKenheiMeR Cornell University 

JaneT e. halliwell JEH Associates Inc 

TRiSTRaM S. leTT INTEGRA Capital Management 

hon. Roy MaClaRen Retired member of Parliament 

peTeR J. niCholSon Council of Canadian Academies 

J. RoBeRT pRiChaRD Torstar Corporation 

williaM pulleyBlanK IBM Global Services 

philip SilleR Eastport Capital Corp. 

ClauDine SiMSon LSI Corporation 

JaniCe STein University of Toronto, Munk Centre 

KaRen uhlenBeCK University of Texas 

haRi VenKaTaChaRya Clineo 

eDwaRD wiTTen Institute for Advanced Study 

Mathematical Sciences Societies Members 

STephen waTT University of Western Ontario and CACS 

Ken JaCKSon University of Toronto and CAIMS 

ToM SaliSBuRy York University and CMS 

MiChael eVanS University of Toronto and SSC 

139

Governance 

Scientific Advisory Panel 2007–2008 

The Scientific Advisory Panel (SAP) provides the scientific 

leadership of the Institute. The SAP, which is chaired by 

the Director, includes the Deputy Director and a rotating 

membership of at least seven distinguished mathematicians 

from Canada and abroad. The panel makes recommendations 

to the Board of Directors on the selection of thematic 

programs and other major activities. 

DAVID BRyDGES received his PhD in 1976 at the University 

of Michigan under the direction of Paul Federbush. He 

held a postdoctoral position at Rockefeller University 

working for James Glimm. His interests are centred on the 

renormalization group with applications to quantum field 

theory, statistical mechanics and probability. In 1978 he 

became Assistant Professor at the University of Virginia. He 

became Professor of Mathematics and Physics in 1981 and 

Commonwealth Chair in 1996. He was recently appointed 

as a Canada Research Chair at the University of British 

Columbia. Brydges received an Alfred P. Sloan Research 

fellowship in 1982. He has given courses in the Troisiéme 

Cycle at Lausanne in 1992, Centre Emile Borel in 1998 and 

the NachDiplom program at ETH, Switzerland. He has 

been the associate editor for Communications of Mathematical 

Physics and Journal of Statistical Physics. Brydges is past 

president of the International Association of Mathematical 

Physics. 

PAM COOK is a Professor of Mathematical Sciences at the 

University of Delaware and Associate Dean of Engineering. 

She also has a secondary appointment as Professor of 

Chemical Engineering at the University of Delaware. She 

received her B.A. in Mathematics from the University of 

Rochester, her PhD. in Applied Mathematics from Cornell 

Universtiy, and was a N.A.T.O. Postdoctoral Scholar at the 

University of Utrecht, The Netherlands. After 10 years as 

a faculty member at the University of California at Los 

Angeles (UCLA) Department of Mathematics she moved 

to the University of Delaware where she was Department 

Chair, and later Associate Dean of Arts and Science. As a 

faculty member she has held visiting appointments at California 

Institute of Technology; the University of Maryland, 

College Park; and the Institute for Mathematics and its 

Applications (I.M.A.) and the Department of Mathematics 

at the University of Minnesota. She is Editor-in-Chief of 

the SIAM (Society of Industrial and Applied Mathematics) 

Journal of Applied Mathematics and she is presently 

secretary of SIAM. She is the coauthor (with J.D.Cole) of 

140 

Transonic Aerodynamics. Her current research is focused on 

modeling complex (viscoelastic) fluids. 

HENRI DARMON received his BSc in Mathematics and 

Computer Science from McGill University in 1987 and his 

PhD in Mathematics from Harvard University in 1991. He 

is currently Professor in the Department of Mathematics 

at McGill University. Prior to his present appointment 

he taught at Princeton University. He has received a 

Sloan Doctoral Dissertation Fellowship, an Alfred P. 

Sloan Research Award, the G. De B. Robinson Award, the 

Coxeter-James Prize of the Canadian Mathematical Society, 

the CRM’s Andre Aisenstadt Prize, NSERC’s E.W.R. 

Steacie Memorial Fellowship, and the Ribenboim Prize of 

the Canadian Number Theory Association. He was elected 

a fellow of the Royal Society of Canada in 2003. Darmon 

served as editor-in-chief (with Niky Kamran) of the Canadian 

Journal of Mathematics and has served on the editorial 

boards of the International Journal of Number Theory, 

Commentari Mathematici Helvetici, the Journal of Number 

Theory, and the Annales des Sciences Mathématiques du 

Quebec. He is a member of NSERC’s Grant Selection Committee 

and of the CMS prize committee. His main research 

interests are in p-adic analysis and the theory of automorphic 

forms with special emphasis on elliptic curves and 

explicit class field theory. 

ERIC FRIEDLANDER is the Henry S. Noyes Professor of 

Mathematics at Northwestern University. He received his 

Ph.D at M.I.T under the direction of Michael Artin. He 

taught at Princeton University for five years, and then 

joined Northwestern University. His research interests 

include algebraic geometry, algebraic K-theory, algebraic 

topology, and representation theory. His recent papers 

can be accessed at www.math.northwestern.edu/~eric/ 

preprints. He has twice served as Chair of the Northwestern 

Mathematics Department and has also served as Academic 

Associate Dean of Science. He is currently a member of the 

Board of Trustees of the American Mathematical Society, 

co-managing editor of the Journal of Pure and Applied 

Algebra, and on the editorial boards of various journals. 

Friedlander gave a surrogate plenary ICM talk in 1986, 

an invited ICM talk in 1998, plenary talks at the A.M.S.- 

Mexicio (2001) and A.M.S.-Spain (2003) international 

meetings. He has organized/co-organized numerous meetings 

and conferences. He was a Humboldt Senior Research 

Scientist and is a member of the American Academy of Arts 

and Sciences.

DAVID JACKSON is a Professor of Mathematics at the University 

of Waterloo. He was an undergraduate at Trinity 

College, Cambridge, and received his PhD in Mathematics 

from the University of Cambridge. He has taught at the 

University of Warwick, Ohio State University, Cornell 

and Cambridge, and has had visiting positions at MIT 

and the Theoretical Division at the Los Alamos National 

Laboratories. He has given a series of advanced seminars 

at Academia Sinica in Beijing. Over the past thirty years 

he has made significant contributions to algebraic combinatorics 

itself, and to the interaction between algebraic 

combinatorics and other areas of mathematics. These 

include representation theory, algebraic geometry, algebra, 

topology, mathematical physics and statistical mechanics. 

He is currently working on approaches to intersection 

theory on the moduli space of curves through algebraic 

combinatorics and, in particular, he is working on Faber’s 

top intersection number conjecture for the moduli space of 

smooth curves. He is a founding Joint Editor-in-Chief of 

the Journal of Algebraic Combinatorics, and is on editorial 

boards of several research journals. He was a member of 

the original committee at Waterloo that initiated plans for 

what eventually became the Fields Institute. He has served 

on one of the CMS prize committees, and has co-organized 

several international meetings and workshops. For a 

number of years he served as a mathematical consultant to 

the Oxford English Dictionary. He is the co-author of two 

research texts, one on enumerative combinatorics and the 

other on the enumerative theory of 2-cell embeddings of 

graphs in orientable and non-orientable surfaces. He is a 

Fellow of the Royal Society of Canada, and a Member of the 

Academy of Mathematical and Physical Sciences. 

BARBARA LEE KEyFITz is serving as Director of the Fields 

Institute for Mathematical Sciences for the period July 

2004-December 2008. In January 2009, she assumes a faculty 

position in mathematics at the Ohio State University. 

Barbara Keyfitz received her undergraduate education in 

mathematics at the University of Toronto and her M.S. and 

Ph.D. from NYU’s Courant Institute. Her research area is 

Nonlinear Partial Differential Equations. She is a Fellow of 

the American Association for the Advancement of Science, 

and the recipient of the 2005 Krieger-Nelson Prize of the 

Canadian Mathematical Society. Until August 2008, she 

was John and Rebecca Moores Professor of Mathematics at 

the University of Houston, which she joined in 1983, following 

appointments at Columbia, Princeton, and Arizona 

State University. She is Treasurer of the International Council 

of Industrial and Applied Mathematics. 

Governance 

JERRy LAWLESS is a Professor of Statistics at University 

of Waterloo. He received his Ph.D. from the University 

of Waterloo in 1969 and has been a faculty member there 

since 1972, serving as Department Chair from 1979-84. His 

research interests include biostatistics, survival and event 

history analysis, reliability, regression methodology, and 

process analysis. He is the author of various papers and 

the book Statistical Models and Methods for Lifetime Data 

(John Wiley and Sons, 2nd edition, 2003) and has served as 

a consultant to industry and government. Dr. Lawless is a 

past Editor of Technometrics and a past President of the Statistical 

Society of Canada. From 1994-2004 he was holder 

of the General Motors-Natural Sciences and Engineering 

Research Council of Canada Industrial Research Chair in 

Quality and Productivity. He is a Fellow of the American 

Statistical Association (1983) and of the Institute of Mathematical 

Statistics (1990), and a recipient of the Gold Medal 

of the Statistical Society of Canada (1999). He was elected a 

Fellow of the Royal Society of Canada in 2000. 

PHILIP MAINI is a Professor of Mathematics at Oxford 

University. He received his B.A. in mathematics from Balliol 

College, Oxford, in 1982 and his DPhil in 1985 under 

the supervision of Prof J.D. Murray, FRS. After completing 

his studies he spent a year as an Assistant Master at Eton 

College before returning to the CMB in 1987 as a Junior 

Research Fellow at Wolfson College, Oxford. In 1988 he was 

appointed Assistant Professor in the Mathematics Department 

at the University of Utah, Salt Lake City for two 

years, before returning to Oxford, initially as a University 

Lecturer and then as Professor and Director of the CMB. 

He is currently on the editorial boards of a large number 

of journals, including serving as the managing editor for 

the Bulletin of Mathematical Biology. He has also been an 

elected member of the Boards of the Society for Mathematical 

Biology (SMB) and European Society for Mathematical 

and Theoretical Biology (ESMBTB). Recently he was 

elected to the Council of the IMA. His research projects 

include the modelling of avascular and vascular tumours, 

normal and abnormal wound healing, collective motion 

of social insects, bacterial chemotaxis, rainforest dynamics, 

pathogen infections, immunology, vertebrate limb 

development and calcium signalling in embryogenesis. He 

has over 170 publications in the field and has held visiting 

positions at the Universities of Ancona, Cambridge, Central 

de Venezuela, Degli Studi Di Modena E Reggio Emila, 

Pierre et Marie Curie (Paris VI), Minnesota, South Florida, 

Washington, Williams College, Queen’sland University of 

Technology, National Tsing Hua University of Taiwan and 

was Distinguished Foreign Visiting Fellow, Hokkaido Uni- 

141

Governance 

versity (2002). He was awarded a Royal Society Leverhulme 

Trust Senior Research Fellowship for 2001-2. He serves on 

the Scientific Advisory Committee of the Fields’ Centre for 

Mathematical Medicine. 

ROBERT RUSSELL is a Professor of Mathematics and Computing 

Science at Simon Fraser University. He received his 

PhD from the University of New Mexico in 1971. After a 

year as Assistant Professor at Colorado State University, he 

joined the faculty at SFU. He has held visiting positions at 

Stanford, University of New Mexico, Universidad Central 

de Venezuela, Imperial College London, Universidad 

Catolica de Chile, University of Auckland, McGill University, 

Universitat de Barcelona, and University of Bath. His 

area of research is scientific computing, primarily adaptive 

methods and software for solving time dependent PDEs. 

His journal editorships include SIAM J. on Numerical 

Analysis, the SIAM Book Series Fundamentals of Algorithms, 

and previously, SIAM J. on Scientific Computing. 

In 2004 he received the Canadian Applied and Industrial 

Mathematics Society Research Prize. His service on various 

committees for SIAM, CAIMS, NSERC, ICIAM, Fields and 

PIMS include being current President of CAIMS, Director 

of the SFU Centre for Scientific Computing, and a member 

of the PIMS Scientific Review Panel. 

JURIS STEPRĀNS is Professor of Mathematics at York 

University and is currently serving as Deputy Director of 

the Fields Institute. He obtained his BMath degree from 

the University of Waterloo in 1977 and completed his PhD 

thesis under the supervision of Franklin D. Tall at the 

University of Toronto in 1982. His research has focussed on 

the applications of set theory to other areas of mathematics, 

notably, group theory, topology, real analysis and the 

theory of Banach spaces. He has held visiting positions at 

various universities and institutions including Dartmouth 

College, the University of Warsaw, the Fields Institute, the 

University of Wisconsin at Madison and Rutgers University. 

He has served in various capacities with the CMS and at 

NSERC. He is an editor of the CEJM. He was elected a Fellow 

of the Fields Institute in 2004. 

CATHERINE SULEM received a Doctorat d’Etat from the 

Université de Paris-Nord in 1983 and held a CNRS position 

at the Ecole Normale Supérieure in Paris before coming to 

the University of Toronto in 1990 as an Associate Professor. 

She was promoted to Professor in 1994. In 1998 she was 

awarded the Krieger-Nelson prize by the Canadian Mathematical 

Society. She works in nonlinear partial differential 

equations arising in physics. Her work uses both analytic 

and numerical methods and has contributed to our under- 

142 

standing of singularities in models of wave propagation. 

She is a coauthor (with her brother Pierre-Louis Sulem) 

of a monograph on “Nonlinear Schrödinger Equation: Self- 

Focusing Instability and Wave Collapse’’ that appeared in 

1999 in the Springer series, Applied Mathematical Sciences. 

Since 2000, she has been Associate editor of the SIAM Journal 

of Mathematical Analysis. 

EVA TARDOS is a Professor of Computer Science at Cornell 

University. She was awarded the George B. Dantzig Prize at 

the SIAM Annual Meeting in 2006. She received the prize 

in recognition for her deep and wide-ranging contributions 

to mathematical programming, including the first strongly 

polynomial-time algorithm for minimum-cost flows, several 

other variants of network flows, integer programming, 

submodularity, circuit complexity, scheduling, approximation 

algorithms, and combinatorial auctions. Tardos’ 

research interest focuses on the design and analysis of efficient 

methods for combinatorial-optimization problems on 

graphs or networks. Her recent work focuses on algorithmic 

game theory, an emerging new area of designing systems 

and algorithms for selfish users. Eva Tardos received her 

Ph.D. at Etvos University in Budapest, Hungary in 1984. 

After teaching at Etvos and the Massachusetts Institute of 

Technology, she joined Cornell in 1989. She is currently a 

member of the American Academy of Arts and Sciences and 

an ACM Fellow. Tardos was a Guggenheim Fellow, a Packard 

Fellow, a Sloan Fellow and an NSF Presidential Young 

Investigator. She received the Fulkerson Prize in 1988. 

NICOLE TOMCzAK-JAEGERMANN received the CRM-Fields- 

PIMS prize in 2006. She is one of the world’s leading 

mathematicians working in functional analysis. She has 

made outstanding contributions to infinite dimensional 

Banach space theory, asymptotic geometric analysis, and 

the interaction between these two streams of modern 

functional analysis. She is one of the few mathematicians 

who have contributed important results to both areas. In 

particular, her work constitutes an essential ingredient in 

a solution by the 1998 Fields Medallist W.T. Gowers of the 

homogeneous space problem raised by Banach in 1932. 

Dr. Tomczak-Jaegermann received her Master’s (1968) and 

Ph.D. (1974) degrees from Warsaw University, where she 

held a position until moving to the University of Alberta in 

1983. There she holds a Canada Research Chair in Geometric 

Analysis. She is a Fellow of the Royal Society of Canada, 

lectured at the 1998 ICM, and has won the CMS Krieger- 

Nelson Prize Lectureship. She has served the Canadian and 

international research community in many ways, including 

her current position on the BIRS Scientific Advisory Board 

and previously as a Site Director of PIMS in Alberta.

EFIM zELMANOV is the Rita L. Atkinson Chair in Mathematics 

at University of California, San Diego. He attended 

Novosibirsk State University, obtaining his PhD in 1980 

having had his research supervised by Shirshov and Bokut. 

His PhD thesis completely changed the whole of the subject 

of Jordan algebras by extending results from the classical 

theory of finite dimensional Jordan algebras to infinite 

dimensional Jordan algebras. Zelmanov described this 

work on Jordan algebras in his invited lecture to the International 

Congress of Mathematicians at Warsaw in 1983. 

In 1980 Zelmanov was appointed as a Junior Researcher at 

the Institute of Mathematics of the Academy of Sciences of 

the USSR at Novosibirsk. By 1986 had had been promoted 

to Leading Researcher. In 1987 Zelmanov solved one of the 

big open questions in the theory of Lie algebras . He proved 

that the Engel identity ad (y)n= 0 in a Lie algebra of zero 

characteristic implies nilpotence. This was a classical result 

for finite dimensional Lie algebras but Zelmanov proved 

that the result also held also for infinite dimensional Lie 

algebras. In 1990 Zelmanov was appointed a professor at 

the University of Wisconsin-Madison in the USA. He held 

this appointment until 1994 when he was appointed to the 

University of Chicago. In 1995 he moved to Yale University 

and in 2002 to the University of California at San Diego. 

In 1991, Zelmanov went on to settle one of the most fundamental 

results in the theory of groups: the restricted 

Burnside problem, which had occupied group theorists 

throughout the 20th century. In 1994 Zelmanov was 

awarded a Fields Medal for this work at the International 

Congress of Mathematicians in Zurich in 1994. He is a Fellow 

of the American Academy of Arts and Sciences and a 

Member of the National Academy of Sciences. 

Governance 

143

Governance 

Industrial Advisory Board 

The Industrial Advisory Board (IAB) includes a rotating 

membership of distinguished mathematicians or users 

of mathematics. The committee reviews major proposals 

for Commercial & Industrial mathematical activity, and 

advises the institute on directions to pursue for the Commercial 

& Industrial mathematics program. 

Members 


DaViD FielD General Motors 


huaxionG huanG York University 

BaRBaRa KeyFiTz Fields Institute 

Daniel KoBleR TmBioscience 

alex KReinin Algorithmics 

MoShe MileVSKy IFID 

KuMaR MuRTy University of Toronto 

philippe RouaneT/BenoiT FleuRy R 2 Financial Technologies 

ToM SaliSBuRy York University 

JuRiS STepRānS Fields Institute 

TaMaS TeRlaKy McMaster University 

144

Principal Sponsoring Universities 2007–2008 

Carleton University 

The School of Mathematics and Statistics at Carleton University 

has a long history of research and graduate study. 

Besides the 36 research faculty, there are ten Distinguished 

Research Professors (including five FRSCs) who, although 

retired, are still very active in research. Areas of research 

include algebra, functional analysis, applied mathematics, 

combinatorics, geometry, logic, number theory, probability 

and statistics (both theoretical and applied). The Laboratory 

for Research in Statistics and Probability, which is 

supported by an NSERC Major Facilities Access Grant, is 

situated in the School. The research activity of the School 

is enhanced by the presence of post-doctoral fellows and 

numerous international visitors. Among the honours 

recently received by members of the School are a Premier’s 

Research Excellence Award, an NSERC Leadership Support 

Initiative Award, and an Early Research Award from 

the Ministry of Research and Innovation. The graduate 

program (MSc and PhD) is joint with the Department of 

Mathematics and Statistics of the University of Ottawa 

with over 80 students on the Carleton campus. In addition, 

the School sponsors (jointly with the School of Computer 

Science and the Department of Systems and Computer 

Engineering at Carleton) a popular Information and Systems 

Science program. The School also offers an MSc in 

biostatistics through the Ottawa-Carleton Collaborative 

Program in Biostatistics. 

The School of Computer Science has a large research effort 

in theoretical computer science. Active areas of research 

include: network computing; geometric computing; digital 

security and cryptography; algorithmic graph theory; provability, 

logics, and verification; stochastic modeling and 

probabilistic algorithms. Two MITACS research projects 

on “Complex Adaptive Networks for Computing and Communication” 

and “Understanding and Mitigating Malicious 

Activity in Networked Computer Systems” are directed by 

Barbeau and Van Oorschot, respectively, and the School 

is the home of the Carleton-Cloakware Security Research 

Lab, headed by a CRC in Network Security (Van Oorschot). 

It is part of the High Performance Computing Virtual 

Laboratory (HPCVL), a four-university consortium with a 

budget of $37 million. Carleton’s HPCVL lab is headed by 

an NSERC-Sun Industrial Research Chair in Applied Parallel 

Computing (Sack). The School offers both a Masters 

and PhD degree in Computer Science, as well as the MSc in 

Governance 

Information and Systems Science (jointly with the School of 

Mathematics and Statistics and the Department of Systems 

and Computer Engineering). 

McMaster University 

McMaster University is a research-intensive, mid-sized 

university located in Hamilton at the west end of Lake 

Ontario. The Mathematics and Statistics Department has 

thirty-eight faculty members, who represent a wide range 

of mathematical research including algebra and number 

theory, analysis, geometry and topology, applied mathematics, 

probability and statistics, and mathematical logic. 

The department has an extensive postdoctoral program 

with about twenty positions each year and a graduate 

program with over eighty students. As one of the founding 

universities of the Fields Institute, McMaster’s contribution 

to the Institute has been substantial. Faculty members from 

McMaster are principal organizers of thematic programs at 

the Fields Institute in each of the next three years; as well 

there have been more than fifteen joint McMaster-Fields 

postdoctoral fellowships. The department has established 

the James Stewart Centre for Mathematics in Hamilton 

Hall, one of McMaster’s two historic buildings, creating 

an integrated teaching, research, and outreach centre to 

enhance the visibility, linkage, and impact of mathematics 

and statistics at McMaster University and the larger community. 

The Department of Computing and Software offers undergraduate 

programs in Software Engineering, including one 

of the first accredited undergraduate software engineering 

programmes in Canada, Software Engineering (Game 

Design), the Mechatronics Engineering program, Computer 

Science, and Business Informatics. At the graduate level, 

the Department offers Master of Applied Science, Master 

of Engineering and Ph.D. programmes in Software Engineering, 

and Master of Science and Ph.D. programmes in 

Computer Science. 

Research initiatives in the department include the 

Advanced Optimization Laboratory, the Algorithms 

Research Group, the Applied Computer Systems Group and 

the Software Quality Research Laboratory. The Department 

is also spearheading the new School of Computational 

Engineering and Science. The Department has a complement 

of 28 faculty members, including three Canada 

Research Chairs. 

145

Governance 

University of Ottawa 

The Department of Mathematics and Statistics at the 

University of Ottawa is an active research department. 

It has about thirty-five faculty members with research 

grants, working in a wide range of areas, including algebra, 

analysis, applied mathematics, cryptography, logic and 

foundations of computing, number theory, statistics, probability, 

and topology. The department is home to a Canada 

Research Chair in mathematical genomics, to a Fellow of 

the Royal Society of Canada (FRSC), and to three holders 

of Ontario Premier’s Researcher Excellence Awards (PREA) 

and/or Early Researcher Awards (ERA). 

The department has a vibrant graduate program joint with 

Carleton University, with currently about seventy graduate 

students at the University of Ottawa. In addition to offering 

MSc and PhD degrees in traditional areas, the department 

also offers an MSc program in Biostatistics, joint with the 

Department of Epidemiology, and an MSc program in 

bioinformatics. 

Besides being a member of the Fields Institute, the 

department is also a member of the Centre de recherches 

mathématiques (CRM). The department is also proud of its 

postdoctoral program, which now provides about six postdoctoral 

positions. The University of Ottawa is a bilingual 

institution in the heart of Canada’s capital. The department 

benefits from its proximity to the government, with a number 

of appointments of adjunct professors who are active 

mathematicians affiliated with Canadian research agencies. 

University of Toronto 

Research and teaching in mathematics is carried out at the 

University of Toronto in the Departments of Computer Science, 

Mathematics, and Statistics, with a combined total of 

over one hundred and forty faculty members. 

The Department of Computer Science was the first 

computer science department established in Canada, and 

is characterized by its breadth of research and teaching 

interests, and the high quality of its faculty and graduate 

students. Faculty members have won many important 

prizes and awards, including the Turing Award (S.A. Cook) 

the Fulkerson Prize in Discrete Mathematics (A. Lehman), 

the IJCAI Award for Research Excellence (G. Hinton, 

R. Reiter) and the Order of Canada (C.C. Gotlieb). The 

department has produced a large proportion of the computer 

science PhD.s in Canada, and has contributed faculty 

members to many departments in Canada and abroad. The 

Department of Computer Science has strong ties with the 

146 

Fields Institute. Members of the department have played 

a central role in several Fields programs, including the 

thematic program on Numerical and Computational Challenges 

in Science and Engineering (2001–2002). 

The Department of Mathematics at the University of 

Toronto is one of the leading mathematics research departments 

in Canada. Mathematics has been taught there since 

1827, and the department’s first PhD was conferred in 

1915 on Samuel Beatty–a student of John Charles Fields, 

whose will established the Fields Medal and after whom 

the Fields Institute is named. Research in the department 

covers a broad spectrum, from mathematical foundations 

to interdisciplinary applications, from number theory and 

geometry to the analysis of shock waves and of financial 

risks. Research excellence is recognized through the highest 

research grant average in Canada, and members of the 

department have delivered addresses at every International 

Congress of Mathematics in the recent past. The department 

is home to the winners of the first three CRM-Fields 

Prizes and to the only mathematician ever awarded the 

Canada Gold Medal for Science and Engineering. The 

department is involved with the Fields Institute at all 

levels–through participation in its workshops and thematic 

programs, in events for high school teachers, and collaborative 

research projects within MITACS. 

The Department of Statistics was established in 1977, and 

offers programs in actuarial science, statistics, and probability. 

The department has a long history of innovation 

and advance in the theory and foundations of statistics, and 

is among the leading theoretical departments in the world. 

It has also been for many years at the forefront of developments 

in statistical computing, and maintains exceptionally 

strong ties with the biostatistics research group in the 

Department of Public Health Sciences. Research activity in 

probability, theoretical statistics, and methods of applied 

statistics is vigorous and growing, and the department has 

recently established a research cluster of Canada Research 

Chairs in data mining and machine learning, jointly with 

the Department of Computer Science. 

University of Waterloo 

The University of Waterloo’s Faculty of Mathematics is 

known for its innovation and leadership in education, 

research, and technology transfer. 

With a population of over forty-five hundred full-time 

undergraduate and four hundred graduate students, and 

one hundred and eighty-five full-time professors, Waterloo

anks as the largest centre for mathematical, statistical 

and computer sciences in the world. The Faculty of Mathematics 

offers a broad range of studies through five units: 

Applied Mathematics, Combinatorics & Optimization, 

Computer Science, Pure Mathematics, and Statistics & 

Actuarial Science. Widely known for its accomplishments 

in computer science, it also has exceptional strength and 

stature in discrete mathematics, applied statistics, and 

actuarial science. Recently, cryptography and quantum 

computation have become major strengths in the Faculty. 

The Faculty of Mathematics generated over $12 million 

in research funding last year. With the University’s liberal 

position on intellectual property, research conducted in the 

Faculty has resulted in several spin-off companies founded 

by professors, students, and graduates. 

Known for its mathematics and computer contests, the 

success of its graduates, and its high standards, the Faculty 

of Mathematics consistently attracts the best students from 

around the world. Waterloo has placed among the top ten 

schools ten times in the past twelve years in the Association 

for Computing Machinery (ACM) International Programming 

Competition. It has been the world champion twice 

(1994, 1999) and North American champion five times 

during that period. As well, the University has placed in the 

top ten in the Putnam Competition fourteen times in the 

past fifteen years, placing first in 1999 and sixth in the most 

recent competition. Waterloo routinely ranks among the 

top three or four schools in terms of the number of students 

who place in the top two hundred in that competition. For 

twelve years in a row, a group of more than three thousand 

senior administrators, company presidents, and academic 

counselors surveyed by Maclean’s Magazine judged the 

University of Waterloo to be the “Best Overall” university 

in Canada. 

University of Western Ontario 

Activity in Mathematics and its applications at the University 

of Western Ontario is focused within the four 

Mathematical Science departments. There is growing 

collaboration between the departments, and links with all 

other sectors of the University. There is substantial interaction 

with and support from the private sector. 

The Department of Applied Mathematics is one of only two 

in the country. The department is research intensive: areas 

of study include mathematical biology, medical science, 

financial mathematics, materials modelling and nanotechnology, 

atomic and high-energy physics, fluid dynamics, 

Governance 

engineering science, environmetrics, cryptography and 

high performance computing using Beowulf clusters. The 

department participates in the Ontario Research Centre 

for Computer Algebra, and in the Imperial Oil Centre for 

Mathematics Education. Members of the department are 

at the forefront of a recently awarded multi-faculty, multiuniversity 

CFI grant for high performance computation. 

The Department of Computer Science offers degrees at 

all levels in computer science, as well as degrees with 

specialization in software engineering. Research activities 

are grouped under the themes of Artificial Intelligence and 

Logic Programming, Graphics and Imaging, Software and 

Systems, Symbolic Mathematical Computation, and Theory 

of Computing, and include projects in cognitive science 

and machine vision, image compression, management 

of distributed systems, symbolic-numeric algorithms for 

polynomials, architectures for mathematical communication 

(MathML and OpenMath), programming languages, 

databases, molecular computing and bioinformatics, and 

automata theory and formal languages. The department 

hosts the Ontario Research Centre for Computer Algebra. 

Major research projects are funded by international, federal, 

provincial and private sector sources. 

Research and teaching in the Department of Mathematics is 

traditionally concentrated in the area of “pure” mathematics. 

The department offers programs at all undergraduate 

and graduate levels of instruction. Its research team is well 

known: faculty members have active research programs 

in homotopy theory, algebraic groups, algebraic K-theory, 

algebraic combinatorics, invariant theory, number theory, 

combinatorial algebra, noncommutative geometry, harmonic 

analysis, complex analysis and complex geometry, 

mathematical physics, and quantization. 

The Department of Statistical and Actuarial Sciences is 

active generally in data analysis and stochastic modelling. 

Data analytic methods include use of visualization in statistical 

analysis and the planning, design and analysis of data 

from a variety of types and sources, including the analysis 

of massive datasets as in fMRI and ultrasound imaging. 

Stochastic modelling includes queueing theory, risk theory, 

mathematical finance, actuarial models for nontraditional 

insurance products, utilization of health care resources, 

environmental impact assessment, reliability, and quality 

control. The department runs a statistical laboratory 

(STATLAB) that carries out contract consulting research. 

147

Governance 

york University 

The Department of Mathematics and Statistics at York 

University is home to a diverse group of scholars, including 

two Canada Research Chairs. Faculty members are active 

in research and publication in several major fields of mathematics 

and statistics. In particular, York has significant 

representation in many general areas including foundations 

of mathematics, probability and stochastic processes, analysis 

(ordinary and partial differential equations, Fourier 

analysis and functional analysis), mathematical modeling 

and numerical analysis, algebra and geometry, financial 

mathematics, and statistics. The quality of scholarly work 

produced by members of the department is attested to by 

its external grant support and recognition. The department 

has consistently been a major recipient of NSERC 

research grants in mathematics and statistics. In a 1995 

study conducted by the U.S.-based Institute for Scientific 

Information, which looked at the scientific impact of papers 

published in top journals, the Department of Mathematics 

at York University ranked second among Canadian mathematics 

departments in citations per paper. In addition, a 

number of York faculty and graduate students are involved 

in the National Centre of Excellence project “The Mathematics 

of Information Technology and Complex Systems” 

(MITACS). The department is equally proud of its thriving 

graduate program. In addition to the regular MA and PhD 

degree programs, the department offers a long-standing 

MA Program for Teachers, which is designed to enhance 

the breadth of knowledge of high school mathematics 

teachers and their effectiveness in the classroom. There is 

in place a Graduate Diploma in Mathematics Education 

offered jointly with the Faculty of Education. An MSc 

program in Industrial and Applied Mathematics began in 

2002. The Department also offers a Graduate Diploma in 

Financial Engineering, in collaboration with the Schulich 

School of Business. This diploma program provides the 

training in finance, mathematics, and computer science 

which is necessary to understand, design and value new 

financial instruments. 

The Department of Computer Science and Engineering at 

York has engaged in a period of sustained growth over the 

past 20 years, evolving from a small teaching department 

in the early 1980s to over 35 faculty today. The department 

offers a full range of undergraduate and graduate programs 

including undergraduate three-year and Honours BA and 

BSc programs, a BASc program, and graduate programs 

leading to MSc and PhD degrees. An optional internship is 

available at all levels which provides students the opportunity 

to experience computer science in an industrial setting. 

148


Donors 

The Fields Institute conducts an annual giving campaign 

each fall to raise funds in support of our scientific and 

educational programs. For further information about donations, 

please visit our website http://www.fields.utoronto. 

ca/aboutus/fundraising/ 

The management and Board of Directors of the Institute 

wish to express their profound thanks to the following, 

whose generous donations in the period April 2007 – March 

2008 are helping to support the work of the Institute. 

2004913 Ontario Ltd. 

Ian Ainsworth 

Abdo Alfakih 

Hermann Brunner 

Arthur J. Carty 

Alison Conway 

Walter Craig & Deirdre Haskell 

John Crow 

Kenneth R. Davidson 

Matt Davison 

Sheila Embleton 

Peter Fillmore 

Tatyana Foth 

Doug Franks 

W.J. Gallop 

John Gardner 

John Goyo 

Gila Hanna 

Hillsdale Investment Management Inc. IFID 

Kenneth Jackson 

Nathan Keyfitz 

Eberhard Kirchberg 

Mikhail Kotchetov 

Trieu Le 

Willis S. McLeese 

M. Mishna 

V. Kumar Murty 

Ping Wong Ng 

George O’Brien 

Josef Paldus 

Doug Park 

Neil Price-Jones 

QWEMA Group Inc. 

Carl & Elaine Riehm 

Mary Salisbury 

Tom Salisbury 

Bhanu Pratap Sharma 

Israel Michael Sigal 

Sigma Analysis & Management Ltd. 

Philip Siller 


Mary Thompson 

Hans Tuenter 

Ignacio Uriarte- Tuero 

Daniel Wevrick 

Graham P. Wright 

Noriko Yui 

Ping Zhou 

Xiaowen Zhou 


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158

Acknowledgements 

The Fields Institute edits and is responsible for the Annual 

Report. However, this project could not be possible without 

the help and input of many individuals. Layout was by UTP 

Print based on a design by Scott Thornley & Company. 

Editorial assistance was provided by Emily Baillie, Barbara 

Keyfitz, Carl Riehm and Juris Steprāns. Administrative 

assistance was provided by Tanya Nebesna and Josephine 

Kavanagh. 

In addition, the Fields Institute would like to thank the following 

people for their contribution; Chris Bauch (Guelph), 

Dietmar Bisch (Vanderbilt), John Braun (Western), Inna 

Bumagin (Carleton), Sue Ann Campbell Waterloo), 

Kevin Cheung (Carleton), Grace Chiu (Waterloo), Jim 

Colliander (Toronto), Benoit Collins (Ottawa), Stephen 

Cook (Toronto), Walter Craig (McMaster), Chandler Davis 

(Toronto), Francois Descouens (York), George Elliott 

(Fields Institute), Al Erickson (SFU), Remus Floricel 

(Regina), John Friedlander (Toronto), George Gadanidis 

(Western), Theirry Giordano(Ottawa), Jinko Graham 

(SFU), Uma Gupta (Fields), Huaxiong Huang (York), 

Ken Jackson (Toronto), Sebastian Jaimungal (Toronto), 

Daniel James (Toronto), Rick Jardine (Western), Daniel 

Jarvis (Nippissing), Gertrud Jeewanjee (CMS), Lisa Jeffrey 

(Toronto), Nicholas Kevlahan (McMaster), Masoud 

Khalkhali (Western), Krista Kostroman (Queen’s), Ilias 

Kotsireas (WLU), Manjunath Krishnapur (Toronto), 

Izabella Laba (UBC), George Labahn (Waterloo), Michael 

Lacey (Georgia Tech), David Langstroth, (Dalhousie), Anna 

Lawniciak (Guelph), Chenkuan Li (Brandon), Kevin Linder 

( Miroslav Lovric (McMaster), Robert McCann (Toronto), 

Eckhard Meinrenken (Toronto), Richard Michael (Fields), 

Moshe Milevsky (IFID), Jamie Mingo (Queen’s), Matthias 

Neufang (Carleton), Monica Nevins (Ottawa), Daniel 

Panario (Carleton), Vladimir Pestov (Ottawa), Irwin Pressman 

(Carleton and CMM), Mary Pugh (Toronto), Nancy 

Reid (Toronto), Bruce Richter (Waterloo), Dan Rosen(R2 

Financial Technologies Inc.), Philippe Rouanet (R2 Financial 

Technologies Inc.), Damien Roy (Ottawa), David Rudd 

(SIGMA), Thomas Salisbury (York), Renate Scheidler 

(Calgary), Romyar Sharifi (McMaster), Siv Sivaloganathan 

(CMM and Waterloo), Theodore Shepherd (Toronto), 

Roberto Solis-Oba (Western), Patrick Speissegger (McMaster), 

Jamie Stafford (Toronto), Brett Stevens (Carleton), 

Paul Szeptycky (York), Eitan Tadmor (Maryland), Tama 

Terlaky (McMaster), Tanya Thompson (Thinkfun Inc.), 

Andrew Toms (York), Murat Tuncali (Nippissing), Thanos 

Acknowledgements 

Tzavaras (Maryland), Balint Virag (Toronto), Stephen 

Watt (Western), David Wehlau (RMC & Queen’s), Brett 

Wick (South Carolina), Graham Wright (CMS), Noriko 

Yui (Queen’s), Mike Zabrocki (York), Mitchell Zimmer 

(Western) 

159

160 

FIELDS INSTITUTE 

for research in Mathematical sciences 

222 College Street 

Toronto, ontario 

Canada, M5T 3J1 

tel 416-348-9710 fAX 416-348-9714 e-MAIl geninfo@fields.utoronto.ca websIte www.fields.utoronto.ca

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