Special Year 2020-21: Geometric and Modular Representation Theory

The problem of classification of perverse sheaves on the quotient $h/W$ for a semisimple Lie algebra $g$ has an explicit answer which turns out to be related to the algebraic properties of induction and restriction operations for parabolic...

The Hecke algebra admits an involution which preserves the standard basis and exchanges the canonical basis with its dual. This involution is categorified by "monoidal Koszul duality" for Hecke categories, studied in positive characteristic in my...

I'll present joint work with Tsao-Hsien Chen on the geometry of real and symmetric matrices. For classical groups, we use hyperkahler geometry to lift the Kostant-Sekiguchi correspondence to an equivariant homeomorphism. As an application, we show...

(work in progress with R. Rouquier) I will present a computational (yet conjectural) method to determine some decomposition matrices for finite groups of Lie type. These matrices encode how ordinary representations decompose when they are reduced to...

Given a representation of a reductive group, Braverman-Finkelberg-Nakajima defined a Poisson variety called the Coulomb branch, using a convolution algebra construction. This variety comes with a natural deformation quantization, called a Coulomb...

For a finite group $G$ one has a process of modular reduction which takes a $KG$-module, over a field $K$ of characteristic zero, and produces a $kG$-module, over a field $k$ of positive characteristic. Starting with a simple $KG$-module its modular...

Reverse plane partitions - or RPPs for short - are order reversing maps of minuscule posets in types ADE. We report on joint work in progress with Elek, Kamnitzer, Libman, and Morton-Ferguson in which we give a type independent proof that RPPs form...

Abstract: in joint work with Leonardo Patimo, we investigate the compatibility of
p-cells with respect to standard parabolic subgroups. Given a p-cell in
a standard parabolic subgroup of a crystallographic Coxeter system,
one can induce the...

Let $G$ be a semi-simple algebraic group over an algebraically closed field $k$ of positive characteristic and let $B$ be a Borel subgroup. The cohomology of line bundles on the flag variety $G/B$ induced by characters of $B$ are important objects...