Annual Report 2005 - Fields Institute - University of Toronto

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most exciting topics at the cutting edge of research in string theory. At Fields, the theme year participants included twelve postdoctoral fellows in both physics and mathematics: Marco Gualtieri, Manfred Herbst, Paul Horja, Nan-Kuo Ho, Shabnam Kadir, Kris Kennaway, Seongchun Kwon, Ruxandra Moraru, Martin Pinsonnault, Ashish Saxena, Alex Yong and Ke Zhu. These postdocs were partly supported by grants from Fields with additional support coming from the personal NSERC grants of various researchers, as well as university teaching support. One of these postdoctoral fellows, Paul Horja, held the Marsden Postdoctoral Fellowship. Another four (Gualtieri, Ho, Pinsonnault and Yong) came with NSERC Postdoctoral Fellowships, which may be taken to indicate both the high quality of the participants and the external attention drawn to the program. A substantial number of graduate students participated in the program, attending the graduate courses and the graduate Summer School (held at PI). The program sponsored approximately forty long term visitors, who spent anywhere from one month to the entire year at Fields and/or Perimeter as program participants. Activities at Fields were funded in part by generous sponsorship from Perimeter Institute. Further funding was also provided by the Connaught Fund of the University of Toronto, the University of Toronto at Scarborough and the National Science Foundation. Of course, the goal of the string program was to stimulate new science, and also to foster discussions between mathematicians and physicists on new directions of research. The full impact of such a program is often difficult to measure and the new ideas which it stimulates usually do not come to fruition immediately. However, it is already clear that this program made a substantial contribution towards advancing the theory and fostering interaction between its different domains and researchers with different backgrounds. There were many positive comments about the string program from other mathematics and physics institutions around the world. As an example of the fruitful interactions, the course and workshop on Mirror Symmetry catalyzed collaboration of two world-class geometers, A. Bondal (Steklov Mathematical Institute) coming from algebraic geometry and W.-D. Ruan (University of Illinois, Chicago) specializing in symplectic geometry. The workshop on Topological Strings provided a stage for intensive discussions between mathematicians and physicists. It was recognized there, for the first time, that the topological string partition function should be regarded as the wave function of some quantum system, both in mathematics T h e m a t i c P r o g r a m s and physics. Ragnar Buchweitz’s course on Homological Algebra catalyzed many discussions around the question of what is the right mathematical language for string theory. Even after his course finished, he and many program participants (including M. Aldi, M. Gaultieri, M. Herbst, K. Hori, P. Horja, D. Page and several students) continued in a series of regular meetings to discuss Maximal Cohen- Macaulay modules and their relation to D-branes in Calabi-Yau and Landau-Ginzburg models. These meetings saw a vigorous exchange in which mathematicians and physicists taught each other what they knew and tried to learn something they wanted to know. These are just a few examples of the numerous collaborations and interactions which were generated by the string program. Program activities continued beyond the period covered by this report. The three-week graduate summer school, Strings, Gravity and Cosmology, took place at Perimeter Institute. This school brought 23 first-class lecturers and roughly 90 students from all over the world for lectures which ran from introductory material to new (as yet unreported) research results. The final event was Strings 05, held on July 11-16, 2005 at the University of Toronto. The “Strings” conferences are the main international meetings in the field of string theory and they are held annually to bring together the world’s leading researchers to present and discuss the latest developments of string theory. Strings 05 marked the first time such meeting was held in Canada! Both these events will be reported on in detail in next year’s annual report. GRADUATE COURSES Course on Mirror Symmetry September–December 2004 Instructor: Kentaro Hori (Toronto) Course on String Theory September–December 2004 Instructor: Amanda Peet (Toronto) Mini-Course on Frobenius Manifolds and Integrable Hierarchies November 8–12, 2004 Instructor: Boris Dubrovin (SISSA, Trieste) Course: Introduction to Homological Algebra January–June 2005 Instructor: Ragnar Buchweitz (Toronto) Fields Institute 2005 ANNUAL REPORT 12
Course on Symplectic Geometry and Topology January–June 2005 Instructor: Boris Khesin (Toronto) Mini-Course on Generalized Geometries in String Theory (Held at Perimeter Institute) February–March 2005 Instructors: Marco Gualtieri (Fields), Yi Li (Caltech) and Mariana Grana (Ecole Polytechnique & Ecole Normale Supérieure) Mini-Course: Toda lattices: Basics and Perspectives March 31 and May 27, 2005 Speakers: Boris Khesin (Toronto), Andrej Marshakov (Lebedev and ITEP, Moscow), and Michael Gekhtman (Notre Dame, IN) WORKSHOPS Workshop on Forms of Homotopy Theory: Elliptic Cohomology and Loop Spaces September 27–October 2, 2004 Organizing Committee: Matthew Ando (UIUC), Michael Hopkins (MIT), Haynes Miller (MIT) and Jack Morava (Johns Hopkins) Workshop on Mirror Symmetry November 19–23, 2004 Held at Perimeter Institute Organizing Committee: Denis Auroux (MIT), Mark Gross (Warwick), Kentaro Hori (Toronto) and Noriko Yui (Queen’s) Workshop on Topological Strings January 10–14, 2005 Organizing Committee: Ezra Getzler (Northwestern), Kentaro Hori (Toronto) and Sheldon Katz (UIUC) Workshop on N=1 Compactifications March 21–25, 2005 Organizers: Michael Douglas (Rutgers), Kentaro Hori (Toronto) and Savdeep S. Sethi (Chicago) Workshop on String Phenomenology March 28–April 1, 2005 Held at Perimeter Institute Organizers: Jan Louis (Center for Mathematical Physics, Hamburg), Robert Myers (Perimeter) and Gary Shiu (Cornell) Workshop on Gravitational Aspects of String Theory May 2–6, 2005 T h e m a t i c P r o g r a m s Organizers: Per Kraus (UCLA), Don Marolf (UCSB) and Amanda Peet (Toronto) Workshop on Schubert Calculus and Schubert Varieties June 8–12, 2005 Organizers: Lisa Jeffrey, Megumi Harada, and Alistair Savage (Toronto); and Alexander Yong (UC Berkeley) Summer School Program on Strings, Gravity and Cosmology June 20–July 8, 2005 Held at Perimeter Institute Organizers: Alex Buchel (Perimeter & UWO), Taejin Lee (Kangwon National U. & APCTP), Robert Myers (Perimeter), Moshe Rozali (UBC) and Gordon Semenoff (UBC) To be reported in the 2006 Annual Report Strings 05 July 11–16, 2005 Held at the University of Toronto Organizers: Alex Buchel (Perimeter), Jaume Gomis (Perimeter), Kentaro Hori (Toronto), Robert Myers (Perimeter), and Amanda Peet (Toronto) To be reported in the 2006 Annual Report LECTURES Coxeter Lecture Series November 15–17, 2004 Nigel Hitchin (Mathematical Inst., Oxford) Open orbits and geometrical structures Instantons and bihermitian metrics Geometry with B-fields January 17–20, 2005 Robbert Dijkgraaf (Inst. for Theoretical Physics, Amsterdam) The mathematics of string theory Topological string theory I and II May 9–11, 2005 Renata Kallosh (Stanford) Towards string cosmology Stabilization of moduli in string theory I and II Distinguished Lecture Series April 4, 5, 7, 2005 Edward Witten (IAS, Princeton) Relativistic scattering theory Gauge symmetry breaking The Quantum Hall Effect Fields Institute 2005 ANNUAL REPORT 13
Page 1 and 2: Fields Institute 2005 ANNUAL REPORT
Page 3 and 4: Institute Profile 2 Message from th
Page 5 and 6: departments in universities and col
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Page 11 and 12: The Geometry of String Theory: Sept
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Page 33 and 34: Thinking of this problem in terms o
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Page 53 and 54: MITACS, NPCDS, the Sustainable Fore
Page 55 and 56: Bo Song (Clemso) Visualization of f
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the property (T) in 2001.) The work
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This conference brought together ma
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Many speakers reported on recent pr
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and former president of the Interna
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S. Mitchell (UBC) An asymptotic fra
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Combinatorics workshop participants
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Workshop participants Each of the i
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Workshop participants Speakers: Ran
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Bruce Allison their work, discuss n
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Poster participants talks, each of
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Workshop on Mathematical Programmin
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University) presented recent result
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volume are Rajendra Bhatia (India),
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SEMINARS Algebraic Combinatorics Se
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Geometry and Model Theory Seminar S
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ments. All of the results obtained
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Vladimir Vinogradov (Ohio) On “co
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parameters - for example, in the ca
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Winter 2004 Meeting of the Canadian
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Special Sessions: Automatic Sequenc
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meeting introduced an Industry/Acad
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The workshop was attended by approx
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tri-annually. MOPTA 05 will be held
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Lowell Aronoff (Cannex Financial Ex
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Kuznetsov, he models each firm usin
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ment returns. The object of the res
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Camp participants Math Camp Program
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This Fields-sponsored symposium was
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Fields Institute Fellows The honour
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Fields Institute Communications Ser
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BARBARA LEE KEYFITZ Director TOM SA
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Scientific Advisory Panel 2004-2005
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and of the Board of Directors of th
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Industrial Advisory Board The Indus
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students at the University of Ottaw
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and graduate students are involved
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F i n a n c i a l S t a t e m e n t
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Fields Institute 2005 ANNUAL REPORT
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