报告题目：Sheaves of modules on atomic sites and discrete representations of topological groups

报告人：李利平教授（湖南师范大学）

报告时间：12月10日9：30-10：20      腾讯会议：366 530 021

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 certain atomic sites, establishing a close relation between representation theory of topological groups and topos theory. In this talk we interpret notions in sheaf theory in the language of 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 Univ.), Li Liang (Lanzhou Jiaotong Univ.), and Fei Xu (Shantou Univ.).

个人简介：李利平，湖南师范大学数学与统计学院特聘教授，博士生导师，湖南省芙蓉学者特聘教授、湖湘高层次人才聚集工程创新人才，湖南省政协委员。2012年在美国明尼苏达大学获博士学位。曾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，在Adv. Math., Trans.Amer. Math. Soc., Selecta Math., J.Lond. Math. Soc.等国际重要SCI期刊发表论文30余篇。曾多次在国内外学术会议上作邀请报告。