Special Year 2020-21: Geometric and Modular Representation Theory

I'll review results and examples of the invariance and monodromy of microlocal sheaves under mutations of their support. Then I'll suggest some problems in geometric representation theory where we would like to apply such techniques.

The talk introduces the Kazhdan-Lusztig categories of representations of affine Lie algebras

I will present a finite-dimensional quiver algebra whose representations are equivalent to the category of Schubert-constructible perverse sheaves on the Grassmannian $Gr(k,n)$. The functor inducing the equivalence is constructed by analyzing the...

Continuation from last time.

For homogeneous affine Springer fibers (those with $G_m$ 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...

I will start by recalling the notion of microlocal perverse sheaves and then briefly explain meldings. The rest of the talk is devoted to explaining the ideas involved in the proof of the codimension-three conjecture.

We discuss modular representations of reductive algebraic groups and then proceed to representations of quantum groups at roots of unity

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...