Special Meeting: Collaborative Research: Affine Hecke algebras, the Langlands Program, Conformal Field Theory and Matrix Models

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The conference ``Affine Hecke algebras, Langlands program, conformal field theory, and matrix models'' will bring together a diverse group of leading mathematicians and physicists and young researchers, to discuss striking recentdevelopments in these fields, and allow experts in one of them tolearn about the others. The conference will consist of three parts: 1) Affine Hecke algebras (1 week) 2) Langlands program (1 week)3) conformal field theory and matrix models (2 weeks).There are numerous and deep connections between these areas, some of whichwere found quite recently. To explore these connections is one ofthe main goals of the conference. Some of the topics to bediscussed in the conference are: representations of affine and double affine Hecke algebras; cyclotomic Hecke algebras; Macdonald theory; geometric representation theory; representations of double loop groups; representations of affine Lie algebras at the critical level; representations of p-adic groups; geometric Langlands conjecturesand their connections to string theory; Seiberg-Witten theory; AdS-CFTcorrespondence; relations between matrix models and string theory. The Langlands program, formulated by R. Langlands in 1967 in hisletter to A. Weil, is a far-reaching program deeply connectingrepresentation theory and number theory. It is crucial forunderstanding central number-theoretic objects called automorphicforms. Affine Hecke algebras are algebraic structures which playa crucial role in the Langlands program. Conformal field theoriesare physical models for the behavior of quantum particles, which are especially tractable mathematically, because of presence of a large amount of symmetry, called conformal symmetry. Such theories (in two spacetime dimensions) are also importantin formulating the basics of string theory. Matrix models is essentially a branch of probability theory, dealing withproperties of random matrices. However, it recently turned out that they have deep applications to string theory. In the last 10 years, there has been significant progress in allfour areas, and it became clear that they are intimatelyrelated. The conference is designed to help experts and youngresearchers (including many women and minorities) to explorethis progress and connections.