Seminar on Geometric and Modular Representation Theory

In the upcoming series of talks we discuss some equivalences by Bezrukavnikov between categories of coherent sheaves on Steinberg varieties and of perverse sheaves on the affine flag variety. In this talk I discuss the decategorified isomorphism...

Wall-crossing functors on the principal block of category OO give an action of the (finite) Hecke category. If one knows enough about the Hecke category, one can deduce the Kazhdan-Lusztig conjectures from the existence of this action. This is a...

The linkage principle says that the category of representations of a reductive group GG in positive characteristic decomposes into "blocks" controlled by the affine Weyl group. We will discuss the beautiful geometric proof of this result that Simon...

Smith theory is a type of equivariant localization with respect to a cyclic group of prime order pp, with coefficients in a field of the same characteristic pp. It has been the source of various recent advances in modular representation theory and...

The talk is about convolution in the setting of geometric representation theory. What are its formal properties? As a starting point, let G be a group and let D(G) be the derived category of constructible sheaves on it. Convolution turns D(G) into a...

Motivated by a formal similarity between the Hard Lefschetz theorem and the geometric Satake equivalence we study vector spaces that are graded by a weight lattice and are endowed with linear operators in simple root directions. We allow field...

Before the "geometric Satake equivalence" there was a decategorified version of it which however contained most of its essential features. In my talk I will talk about some of the ideas which have led to this theory. In particular I will explain the...

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...

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.