Perverse sheaves and intersection cohomology are central objects
in geometric representation theory. This talk is about their
long-lost K-theoretic cousins, called K-motives. We will discuss
definitions and basic properties of K-motives and explore...
The goal of this talk is two-fold. We state a parabolic version
of the two realizations theorem and sketch a proof. This version
relates Iwahori-constructible sheaves on parabolic affine flag
variety to coherent sheaves on a parabolic version of the...
I will start with a few comments on the proof of the equivalence
presented in the previous talks. Then I will focus on the
description of the abelian category of perverse sheaves
on the affine flag variety on the coherent side, where the answer
In this talk we will begin the discussion of the results in
Bezrukavnikov's "On Two Geometric Realizations of the Affine Hecke
algebra". We will put all the previous tools described in this
series of talks together to construct the equivalence of...
We will discuss the following theorems concerning colimits taken
in the infinity-category of monoidal DG-categories. (No familiarity
with infinity-categories will be required or assumed.) The affine
Hecke category is the monoidal colimit of its...
A theorem of Bernstein identifies the center of the affine Hecke
algebra of a reductive group GG with the Grothendieck
ring of the tensor category of representations of the dual
group G?G?. Gaitsgory constructed a functor which
This is the second in a series of talks on "two realizations."
We discuss equivariantization and de-equivariantization for a
group GG, which relate categories with GG-actions and
categories with RepG-actions, and how this relates to the notion
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