Program

During the last thirty years, the representation theory of infinite-dimensional Lie algebras has been one of the most prolific areas of modern mathematics, and has developed deep connections with many other areas of pure mathematics and mathematical physics, including algebraic geometry, integrable systems, quantum field theory, statistical mechanics, and combinatorics. This program will discuss recent progress in the representation theory of infinite-dimensional algebras and superalgebras and their applications to other fields. There will be two major underlying themes in the program: interrelations between mathematical and physical perspectives on representation theory, and the interplay between algebraic and geometric methods. The main topics are:Representation theory of infinite-dimensional Lie algebras, such as, the Virasoro algebra, Kac-Moody algebras; W-algebras; quantum groups; vertex and conformal algebras; Lie superalgebras;Applications to conformal field theory, statistical mechanics, integrable systems, string theory and its generalizations;Interrelations with algebraic geometry (moduli spaces, geometric Langlands correspondence, etc.), theory of automorphic functions, combinatorics and representation theory of reductive Lie groups.