Conference on Gauge Theory and Representation Theory

规范理论与表示论会议

基本信息

批准号：
0738196
负责人：
Robert MacPherson
金额：
$ 2.4万
依托单位：
Institute For Advanced Study
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2007
资助国家：
美国
起止时间：
2007-09-01 至 2008-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0738196&HistoricalAwards=false
关键词：
Conference Gauge Theory Representation

项目摘要

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.

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通过代数几何形状的方法表示； 2）几何兰兰兹二重性程序； 3）Quantumfield理论的双重性，例如$ s $ duality和镜像对称性。 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. 以下研究人员在研讨会上同意了Toparticipate：A。Beilinson，A。Braverman，T.Bridgeland，M。Douglas，D。Gaitsgory，E。Frenkel，A。Kapustin，M。 Liu，G。Moore，H。Nakajima，N。Nekrasov，N。Saulina和E.Witten。会议的另一个重要目的是在相邻领域和研究生和研究生的上述每个领域中积累了知识的传播。因此，我们期望它有助于这些领域的新方法的综合，并形成新一代的研究人员。