Special Year 2020-21: Geometric and Modular Representation Theory

The theta correspondence of Roger Howe gives a way to connect representations of different classical groups. We aim to geometrize the theta correspondence for groups over finite fields in the spirit of Lusztig's character sheaves. Given a reductive...

This talk will be an exposition of a recent paper of Bezrukavnikov-Gaitsgory-Mirkovic-Riche-Rider giving an Iwahori-Whittaker model for the Satake category. The main point is that their argument works for modular coefficients. I will give some...

The modular representation theory of a finite group naturally breaks into different pieces called blocks, and the defect of a block is a sort of measure of its complexity. I will recall some basic aspects of this theory, and then give the complete...

This is the last talk towards understanding Bezrukavnikov-Finkelberg's derived geometric Satake equivalence. With the preparations from previous talks, we will introduce two filtrations: a topological filtration on the equivariant cohomology and an...

The decomposition of the reduction of a Deligne--Lusztig character as a sum of Weyl modules is given by Jantzen's formula. In the case of $SL_2(F_q)$ the formula can be proved by a direct computation, and as a result we will see that the entries in...

This is the third talk in a series of three talks on the derived Satake equivalence. I will give an overview of the article of Bezrukavnikov and Finkelberg which explains how the equivariant derived category of the affine Grassmannian can be...

This is the second talk in a series of three talks on the derived Satake. I will give an overview of an article by Ginzburg which laid the foundational ideas for this equivalence.

In this talk I hope to explain how the representation theory of $GL_n(F_q)$ (with q being a power of p) in char. p, and also in mixed characteristic $(0,p)$, plays an important role in the theory of Galois representations and the Langlands program...

This is the first talk in a series of three talks towards understanding Bezrukavnikov-Finkelberg's derived geometric Satake equivalence. In this talk, we recall the geometry of equal characteristic affine Grassmannians and some of the ingredients of...