I will report on a joint work in progress with K. Coulembier and
V. Ostrik. We show that a symmetric tensor category in
characteristic p>0 admits a fiber functor to the Verlinde
category (semisimplification of Rep(Z/p)) if and only if it
has...
I will report on a project joint with Roman Bezrukavnikov (and
partly with Laura Rider) aiming at constructing a variant for
positive-characteristic coefficients of the equivalence constructed
by Bezrukavnikov in "On two geometric realizations of an...
For homogeneous affine Springer fibers (those
with GmGm symmetry), we realize them as Lagrangian cycles
inside ambient symplectic varieties, and make sense of microlocal
sheaves supported on these affine Springer fibers. We also propose
a...
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
is...
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
categrorifies this...
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
of...
