Conference on Gauge Theory and Representation Theory

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This proposal for a conference to be held at IAS in theframework of the Special Year ``New Connections ofRepresentation Theory to Algebraic Geometry and Physics''.Recent developments in representation theory, algebraic geometryand quantum field theory have uncovered strong connectionsbetween the following major branches of research: 1)Kazhdan-Lusztig theory, understood broadly as study of numericalinvariants of representations by methods of algebraic geometry;2) geometric Langlands duality program; 3) dualities of quantumfield theory such as $S$-duality and mirror symmetry. Inparticular, many of the relevant constructions have, or areexpected to have, natural explanations in the framework of4-dimensional supersymmetry gauge theory.The conference will bring together representation theorists,algebraic geometers and theoretical physicists whose work leadsto such connections, with the goal of advancing each of thesubjects, and achieving a deeper understanding of their roots ingauge theory. The following researchers have agreed toparticipate 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 ofknowledge accumulated in each of the above mentioned areas amongexperts in the neighboring fields and graduate students. Thuswe expect it to contribute to a synthesis of the new methods inthese fields, and to forming a new generation of researchers.