The previous talk in this series is here.
This will be a course on the representation theory of algebraic groups, and relations to the representation theory of symmetric groups. Reductive algebraic over finite fields and their algebraic closures are fascinating objects: one the one hand they look like Lie groups, but on the other hand they look like finite groups. Thus they mix two very different areas of mathematics. I will outline some of the basic theory, and then move on to questions of current interest.
Ting Xue’s lectures in the previous week will provide essential background. I will aim to point out connections to the modular representation theory of finite groups. Although not essential, some background in algebraic geometry (e.g. the first three chapters of Hartshorne’s Algebraic Geometry) will help with understanding latter parts of the course.
This video was produced by the Australian Mathematical Sciences Institute as part of the AMSI Winter School 2022.