Future Directions in Representation Theory

该奖项资助美国研究人员参加将于2017年12月4日至8日在悉尼大学举行的题为代表理论未来方向的国际研究会议。广义地讲，表象理论的领域涉及到理解线性系统的对称性。“对称性”的概念通过群的数学概念变得精确；给定一个抽象的群，人们可以问这个群如何通过向量空间上的线性变换来实现。这门学科起源于代数，但当前表示理论的发展涉及到其他数学领域的输入，如几何和拓扑学，以及来自物理学的想法。本次会议汇聚了来自不同研究背景的专家，报告新的发展并交流意见。当前在表征理论前沿的许多发展都依赖于一系列不同的工具，这些工具的起源可能是几何的、绝对的或同源的。相反，表象理论的问题推动了数学和数学物理领域的一些新发展。这次会议的特点是演讲者的工作位于表征理论和这些邻近学科的界面上，他们的研究计划预示着表征理论未来可能发展的方向。具体的主题包括：(I)辛对偶和数学物理；(Ii)分类和范畴作用；(Iii)表示论中的上同调方法；(Iv)奇偶层和索尔盖尔双模。在这笔资金的支持下，美国研究人员将有机会与一些世界领先的表征理论专家互动，并与澳大利亚和其他国家的同行研究人员进行接触。会议网页为：https://sites.google.com/site/ausreptheory/conference2017.

This award funds participation by US researchers in an international research conference entitled Future Directions in Representation Theory, to be held at the University of Sydney from December 4-8, 2017. Broadly speaking, the field of representation theory deals with understanding symmetries of linear systems. The notion of "symmetries" is made precise by the mathematical concept of a group; given an abstract group, one can ask how that group can be realized via linear transformations on a vector space. This subject has algebraic origins, but current developments in representation theory involve input from other areas of mathematics, such as geometry and topology, as well as ideas from physics. This conference brings together experts from diverse research backgrounds to report on new developments and exchange ideas. Many current developments at the frontiers of representation theory rely on a diverse array of tools whose origins may be geometric, categorical, or homological in nature. Conversely, questions from representation theory have motivated a number of new developments in neighboring fields of mathematics and mathematical physics. This conference features speakers whose work lies at the interface of representation theory and these neighboring subjects, and whose research programs are indicative of the directions along which representation theory may develop in the future. Specific topics include: (i) symplectic duality and mathematical physics; (ii) categorification and categorical actions; (iii) cohomological methods in representation theory; (iv) parity sheaves and Soergel bimodules. US researchers supported by this funding will have the opportunity to interact with some of the world's leading experts in the representation theory, as well as to make contacts with peer researchers from Australia and other nations. The conference webpage is: https://sites.google.com/site/ausreptheory/conference2017.