# Seminars Sorted by Series

## Virtual Workshop on Recent Developments in Geometric Representation Theory

### Virtual Workshop on Recent Developments in Geometric Representation Theory

The theta correspondence of Roger Howe gives a way to connect representations of different classical groups. We aim to geometrize the theta correspondence for groups over finite fields in the spirit of Lusztig's character sheaves. Given a reductive...

### Virtual Workshop on Recent Developments in Geometric Representation Theory

There are two categorical realizations of the affine Hecke algebra: constructible sheaves on the affine flag variety and coherent sheaves on the Langlands dual Steinberg variety. A fundamental problem in geometric representation theory is to relate...

### Virtual Workshop on Recent Developments in Geometric Representation Theory

The geometric Satake equivalence establishes a link between two categories: the category of spherical perverse sheaves on the affine Grassmannian and the category of representations of the Langlands dual group. It has found many important...

### Virtual Workshop on Recent Developments in Geometric Representation Theory

We explain an equivalence of categories between a module category of quiver Hecke algebras associated with the Kronecker quiver and a category of equivariant perverse coherent sheaves on the nilpotent cone of type A. This provides a link between two...

### Virtual Workshop on Recent Developments in Geometric Representation Theory

The Picard group of the stable module category of a finite group plays a role in many parts of modular representation theory. It was calculated when the group is an abelian $p$-group, by pioneering work of Dade in the 1970's, and a classification...

### Virtual Workshop on Recent Developments in Geometric Representation Theory

We construct an explicit isomorphism between certain truncations of quiver Hecke algebras and Elias-Williamson's diagrammatic endomorphism algebras of Bott-Samelson bimodules. As a corollary, we deduce that the decomposition numbers of these...

### Virtual Workshop on Recent Developments in Geometric Representation Theory

### Virtual Workshop on Recent Developments in Geometric Representation Theory

Categorification of integrable representations of quantum Kac--Moody algebras is a relatively well-developed subject nowadays, which has found several applications, in particular to low-dimensional topology. The story outside of the integrable world...

### Virtual Workshop on Recent Developments in Geometric Representation Theory

Algebraic topologists talk about an elevator from characteristic zero to characteristic p, with infinitely many floors in between called chromatic levels. I think you could "do representation theory" at any of these levels. I once tried to explore...

### Virtual Workshop on Recent Developments in Geometric Representation Theory

I will review certain stabilization phenomena in the characteristic zero representation theory of general linear and symmetric groups as the rank tends to infinity. Then I will give a survey of some results and conjectures about analogs of these in...

### Virtual Workshop on Recent Developments in Geometric Representation Theory

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...

### Virtual Workshop on Recent Developments in Geometric Representation Theory

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...

### Virtual Workshop on Recent Developments in Geometric Representation Theory

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...

### Virtual Workshop on Recent Developments in Geometric Representation Theory

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...

### Virtual Workshop on Recent Developments in Geometric Representation Theory

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...

### Virtual Workshop on Recent Developments in Geometric Representation Theory

(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...

### Virtual Workshop on Recent Developments in Geometric Representation Theory

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...

### Virtual Workshop on Recent Developments in Geometric Representation Theory

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...

### Virtual Workshop on Recent Developments in Geometric 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...