Conference on Gauge Theory and Representation Theory

Institute For Advanced Study, Princeton NJ

Investigators

Abstract

This proposal for a conference to be held at IAS in the framework of the Special Year ``New Connections of Representation Theory to Algebraic Geometry and Physics''. Recent developments in representation theory, algebraic geometry and quantum field theory have uncovered strong connections between the following major branches of research: 1) Kazhdan-Lusztig theory, understood broadly as study of numerical invariants of representations by methods of algebraic geometry; 2) geometric Langlands duality program; 3) dualities of quantum field theory such as $S$-duality and mirror symmetry. In particular, many of the relevant constructions have, or are expected to have, natural explanations in the framework of 4-dimensional supersymmetry gauge theory. The conference will bring together representation theorists, algebraic geometers and theoretical physicists whose work leads to such connections, with the goal of advancing each of the subjects, and achieving a deeper understanding of their roots in gauge theory. The following researchers have agreed to participate in the workshop: A. Beilinson, A. Braverman, T. Bridgeland, M. Douglas, D. Gaitsgory, E. Frenkel, A. Kapustin, M. Liu, G. Moore, H. Nakajima, N. Nekrasov, N. Saulina and E. Witten. Another important purpose of the conference is dissemination of knowledge accumulated in each of the above mentioned areas among experts in the neighboring fields and graduate students. Thus we expect it to contribute to a synthesis of the new methods in these fields, and to forming a new generation of researchers.