报告题目：Sheaves over Categories with Atomic Topology and Discrete Representations of Topological Groups

主 讲 人：李利平

单 位：湖南师范大学

时 间：5月20日20:30

腾 讯 ID：920 725 588

摘 要：

It is well known that the category of discrete G-sets of a topological group G is equivalent to the category of sheaves of sets over a certain orbit category equipped with atomic topology. This result establishes an important relation between representation theory of topological groups, representation theory of categories, and topos theory. In this talk, I will characterize sheaves of modules over arbitrary categories equipped with atomic topology, sheafification functor, and sheaf cohomology in terms of notions in representation theory of categories, and obtain equivalences between sheaf categories and Serre quotients of representation categories. Furthermore, via applying the Nakayama functor, we classify simple discrete representations of a few important topological groups such as infinite symmetric groups, infinite general linear groups over a finite field, the automorphism group of the poset of rational numbers. This work is joint with Zhenxing Di (Northwest Normal University), Li Liang (Lanzhou Jiaotong University), and Fei, Xu (Shantou University).

简 介：

李利平，湖南师范大学数学与统计学院教授、博士生导师。2012年毕业于美国明尼苏达大学，获博士学位。2012-2015年任加州大学河滨分校数学系访问助理教授。主要研究领域为代数表示论与表示稳定性理论，主要成果发表在Adv. Math.，J. Lond. Math. Soc.，Trans. A. M. S.，Selecta Math.， J. Alg.，等知名期刊上。