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

Massachusetts Institute Of Technology, Cambridge MA

Investigators

Abstract

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 recent developments in these fields, and allow experts in one of them to learn 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 which were found quite recently. To explore these connections is one of the main goals of the conference. Some of the topics to be discussed 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 conjectures and their connections to string theory; Seiberg-Witten theory; AdS-CFT correspondence; relations between matrix models and string theory. The Langlands program, formulated by R. Langlands in 1967 in his letter to A. Weil, is a far-reaching program deeply connecting representation theory and number theory. It is crucial for understanding central number-theoretic objects called automorphic forms. Affine Hecke algebras are algebraic structures which play a crucial role in the Langlands program. Conformal field theories are 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 important in formulating the basics of string theory. Matrix models is essentially a branch of probability theory, dealing with properties 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 all four areas, and it became clear that they are intimately related. The conference is designed to help experts and young researchers (including many women and minorities) to explore this progress and connections.