Seminar on Geometric and Modular Representation Theory

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 moderate...

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 conjectural...

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...