Some solved and unsolved problems in representation theory of finite groups
报告题目(Title)：Some solved and unsolved problems in representation theory of finite groups
报告人(Speaker)：Lleonard Rubioy Degrassi（University of Murcia）
地点(Place)：后主楼1124
时间(Time)：2019年10月11日 16:00-17:00
邀请人(Inviter)：刘玉明
报告摘要
Since the work of Galois, finite groups have played a major role in mathematics. A main area of research is representation theory which is the study of linear representations of a finite group $G$, or equivalently, the module actions of the group algebra $kG$ on a vector space.
In this talk I will discuss some classical results and some open conjectures in representation theory of finite group.
In the first part I will state some of the main results of representation theory over the field of complex numbers and I will then highlight when this differs from the modular setting, that is, over a field of prime characteristic.
In the second part I will introduce some notions of category theory in order to compare the module categories of blocks using Morita equivalences. I will also discuss the famous tame-wild dichotomy for blocks of group algebras and the classification up to Morita equivalences due to Erdmann.
Finally, I will state two open problems: Donovan's and Auslander-Reiten's conjectures and some recent progress.
