报告时间：2021年4月26日, 10:00-11:00

报告地点：腾讯会议：471 894 852

报告人：李利平教授（湖南师范大学） 

报告摘要：Let G be a topological group. It is well known that the category of discrete G-sets is a topos (that is, a category of sheaves over a certain orbit category associated to G and equipped with atomic topology). This result establishes an important relation between representation theory of topological groups, representation theory of categories, and sheaf 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 torsion theory, and obtain equivalences between sheaf categories and Serre quotient 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 University), Li Liang (Lanzhou Jiaotong University), and Fei, Xu (Shantou University).

报告人简介：李利平，99年本科毕业于清华大学化学系，12年从明尼苏达大学获数学博士学位，12-15年在加州大学河滨分校任访问助理教授，15年至今任湖南师范大学数学与统计学院教授。主要研究代数表示论表示稳定性理论，在Adv. Math., Trans. Amer. Math. Soc., Selecta Math., J. Lond. Math. Soc., J. Algebra等发表论文30余篇，证明了复数域上的artinian猜想、一般线性群的同余群的同调群的线性稳定界限等重要猜想，成果被斯坦福、芝加哥、密歇根、威斯康辛等大学同行多次在报告与讲座中介绍。现任学院副院长、湖南省政协委员，入选湖南省芙蓉学者特聘教授计划。

欢迎参加！

邀请人：白占强, 董超平