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$J. Phys. A: Math. Gen. 17 (1984) - PIMS$

$Alberta Colleges Math Conf and North-South Dialogue Event T - PIMS$

1 PRIMA 2013 AbstractsContents1 Public Lectures 22 Plenary Lectures 23 Special Sessions 4Special Session 1A Glimpse of Stochastic Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Special Session 2Algebraic and Complex Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Special Session 3Algebraic Topology and Related Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Special Session 4Applications of Harmonic Maps and Submanifold Theory . . . . . . . . . . . . . . . . . . . 8Special Session 5Combinatorics and Discrete Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Special Session 6Geometric Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Special Session 7Geometric Aspects of Semilinear Elliptic Equations: Recent Advances & Future Perspectives 15Special Session 8Hyperbolic Conservation Laws and Related Applications . . . . . . . . . . . . . . . . . . . 17Special Session 9Inverse Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Special Session 10Kinetic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Special Session 11Mathematical Fluid Dynamics and Related Topics . . . . . . . . . . . . . . . . . . . . . . 22Special Session 12Mathematics of String Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Special Session 13Measurable and Topological Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Special Session 14Multiscale Analysis and Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Special Session 15Number Theory and Representation Theory . . . . . . . . . . . . . . . . . . . . . . . . . 29Special Session 16Operator Algebras and Harmonic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 31Special Session 17Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Special Session 18Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Special Session 19Representation Theory and Categorification . . . . . . . . . . . . . . . . . . . . . . . . . 38Special Session 20Singularities in Geometry and Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Special Session 21Symplectic Geometry and Hamiltonian Dynamics . . . . . . . . . . . . . . . . . . . . . . 42Special Session 22Symplectic Geometry and Mathematical Physics . . . . . . . . . . . . . . . . . . . . . . . 43Special Session 23Triangulated Categories in Representation Theory of Algebras . . . . . . . . . . . . . . . . 454 Contributed Talks 47Contributed Talks Group 1Geometry and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Contributed Talks Group 2Algebra and Number Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Contributed Talks Group 3Discrete Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Contributed Talks Group 4Computational Mathematics & Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 53Contributed Talks Group 5Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Contributed Talks Group 6Probability and Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2 PRIMA 2013 Abstracts1 Public LecturesComputers and mathematics:prospectsRon GrahamUniversity of California, San Diego, USAgraham@ucsd.eduproblems andThere is no question that the recent advent of the moderncomputer has had a dramatic impact on what mathematiciansdo and on how they do it. However, there is increasingevidence that many apparently simple problemsmay in fact be forever beyond any conceivable computerattack. In this talk, I will describe a variety of mathematicalproblems in which computers have had, may have orwill probably never have a significant role in their solutions.Of triangles, gas, prices and menCédric VillaniUniversité de Lyon and Institut Henri Poincaré, Francevillani@ihp.frThe story of mathematical progress coming from the accidentalencounter of three different fields which seemedto have hardly anything in common.2 Plenary LecturesRandom walks and percolationMartin BarlowUniversity of British Columbia, Canadabarlow@math.ubc.caAround 1960 de Giorgi, Moser and Nash proved regularityfor the heat equation associated with divergence formPDE:∂u∂t = Lu, u = u(x, t), x ∈ Rd , t > 0. (1)Here L = ∇a∇, where a = a ij (x) is uniformly elliptic. Inthe special case when a = ρ(x)I, (1) describes heat flowin a medium of varying conductivity ρ, and uniformlyelliptic means that ρ is bounded away from 0. If on theother hand Z = {x : ρ(x) = 0} ̸= ∅, then the zero regionscan form barriers, and the behaviour of solutions to (1)will depend on the detailed geometry of Z.As an approach to problems of this kind, one can considerdiscrete approximations to (1). One such is percolationon the Euclidean lattice Z d , which was introduced byBroadbent and Hammersley in 1957. Let p be a fixedprobability between 0 and 1. Each bond in Z d is retainedwith probability p, and removed with probability 1 − p,independently of all the others. If p is larger than somecritical value p = p c(d) then the resulting graph has aunique infinite connected component C. De Gennes in1976 called the random walk on C the ‘the ant in thelabyrinth’. The problem is related to the heat equation,since if p(n, x, y) is the probability that a random walker(‘the ant’), starting at x, is at y at time n, then p satisfiesa discrete version of (1).The PDE techniques of Nash and Moser have proved veryuseful in these contexts. I will discuss recent progress onthese models, and in particular will discuss the proof ofGaussian bounds for p n, and a central limit theorem forthe (rescaled) random walk.The Mathematics of CrimeAndrea BertozziUniversity of California, Los Angeles, USAbertozzi@math.ucla.eduThere is an extensive applied mathematics literature developedfor problems in the biological and physical sciences.Our understanding of social science problems froma mathematical standpoint is less developed, but alsopresents some very interesting problems. This lectureuses crime as a case study for using applied mathematicaltechniques in a social science application and coversa variety of mathematical methods that are applicable tosuch problems. We will review recent work on agent basedmodels, methods in linear and nonlinear partial differentialequations, variational methods for inverse problemsand statistical point process models. From an applicationstandpoint we will look at problems in residentialburglaries and gang crimes. Examples will consider bothbottom up and top down approaches to understandingthe mathematics of crime, and how the two approachescould converge to a unifying theory.The exact renormalization group flowWeinan EPeking University, China and Princeton University, USAweinan@math.princeton.eduRenormalization and renormalization group is the mostimportant theoretical advance in the second half of thelast centrury in physics. At its heart is a mathematicaltool for handling singularities, infinities and complexsystems involving multiple scales. Yet at the mathematicallevel, it still remains to be somewhat of a mysterious,ad hoc and even dubious procedure. We will discussour effort to develop the mathematical foundationof the exact renormalization group flow. We will startwith some simple examples (central limit theorem, extremestatistics, homogenization) and then discuss applicationsto stochastic PDEs, quantum field theory andturbulent transport. This is joint work with Hao Shen,Yajun Zhou and Qingyun Sun.Sphere packings, symplectic lattices and RiemannsurfacesJun-Muk HwangKorea Institute for Advanced Study, Koreajmhwang@kias.re.krSymplectic lattices are lattices in Euclidean space withcertain extra-symmetries associated to Hermitian forms.They correspond to principally polarized abelian varietiesin algebraic geometry. Classical examples are given by periodlattices of compact Riemann surfaces.Our theme is the density of sphere packing for symplecticlattices. In their seminal work in 1994, Buser andSarnak showed that peorid lattices of compact Riemannsurfaces give remarkably poor sphere packing. FollowingBuser-Sarnak’s work, many interesting relations betweenthe density of sphere packing for symplectic lattices andalgebro-geometric properties of corresponding abelian varietieshave been discovered. We will give an overview ofthis subject with a report on a recent work on period latticesof Prym varieties, another important class of symplecticlattices arising from algebraic geometry.The classification of subfactors of small indexVaughan JonesVanderbilt University, USAvfr@math.berkeley.eduStarting with the definition of a von Neumann algebra Iwill survey old and new developments in the index theory
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Page 58 and 59: 11 PRIMA 2013 AbstractsEnumerating,
Page 60 and 61: 13 PRIMA 2013 AbstractsRyuhei Uehar
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Page 72 and 73: 25 PRIMA 2013 AbstractsPedram Hekma
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Page 86 and 87: 39 PRIMA 2013 AbstractsAlexander Mo
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Page 92 and 93: 45 PRIMA 2013 AbstractsJian ZhouTsi
Page 94 and 95: 47 PRIMA 2013 AbstractsJiaqun WeiNa
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51 PRIMA 2013 AbstractsJongyook Par
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53 PRIMA 2013 AbstractsPancyclicity
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55 PRIMA 2013 AbstractsEfficient nu
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57 PRIMA 2013 Abstractsand fountain
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59 PRIMA 2013 Abstractsformula esti
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