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.
For more information about this event, please email
infinidim@msri.org
The workshops for this program are:
Geometric Aspects of the Langlands Program
March 18, 2002
to March 22, 2002
Discussion of the important developments in the geometric Langlands correspondence in the last few years
Conformal Field Theory and Supersymmetry
April 15, 2002
to April 26, 2002
The first week will focus on Infinite-dimensional Algebras, Conformal Field Theory and Integrable Systems, and the second week would be devoted to Supersymmetry in Mathematics and Physics.
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