Conference on Gauge Theory and Representation Theory

关于在国际科学院举行"表示论与代数几何和物理的新联系“特别年的框架内召开一次会议的建议，表示论、代数几何和量子场论的最新发展揭示了以下主要研究分支之间的密切联系：1）Kazhdan-Lusztig理论，广义上理解为用代数几何方法研究表示的数值不变量; 2）几何Langlands对偶程序，3）量子场论的对偶性，如$S$-对偶性和镜像对称性。 特别是，许多相关的结构已经或有望在四维超对称规范理论的框架中得到自然的解释。会议将汇集表示理论家、代数几何学家和理论物理学家，他们的工作导致了这种联系，目标是推进每个学科，并更深入地理解它们在规范理论中的根源。 以下研究人员已同意参加研讨会：A. Beilinson，A.作者：Braverman，T.道格拉斯，D. Gaitsgory，E. Frenkel，A. Kapustin，M. Liu，G.摩尔，H. Nakajima，N. Nekrasov，N. Saulina和E.维滕。会议的另一个重要目的是传播在上述每个领域积累的知识，包括邻近领域的专家和研究生。 因此，我们期望它有助于综合这些领域的新方法，并形成新一代的研究人员。

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.