Seminars Sorted by Series

Let G be a simply-connected complex semisimple algebraic group and let C be a smooth projective curve of any genus. Then, the moduli space of semistable G-bundles on C admits so called determinant line bundles. E. Verlinde conjectured a remarkable...

Let G be a simply-connected complex semisimple algebraic group and let C be a smooth projective curve of any genus. Then, the moduli space of semistable G-bundles on C admits so called determinant line bundles. E. Verlinde conjectured a remarkable...

Let G be a simply-connected complex semisimple algebraic group and let C be a smooth projective curve of any genus. Then, the moduli space of semistable G-bundles on C admits so called determinant line bundles. E. Verlinde conjectured a remarkable...

Let G be a simply-connected complex semisimple algebraic group and let C be a smooth projective curve of any genus. Then, the moduli space of semistable G-bundles on C admits so called determinant line bundles. E. Verlinde conjectured a remarkable...

Let G be a simply-connected complex semisimple algebraic group and let C be a smooth projective curve of any genus. Then, the moduli space of semistable G-bundles on C admits so called determinant line bundles. E. Verlinde conjectured a remarkable...

Let G be a simply-connected complex semisimple algebraic group and let C be a smooth projective curve of any genus. Then, the moduli space of semistable G-bundles on C admits so called determinant line bundles. E. Verlinde conjectured a remarkable...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

(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...

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...

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...

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...

I will survey some applications of Ramanujan Graphs in theoretical computer science, as well as some of the work they have inspired. 

Along the way, I'll explain how they impacted the thinking and assumptions of my generation.

I'll discuss spectral gaps in the following contexts:
- d-regular graphs
- locally symmetric spaces e.g. hyperbolic manifolds
- finite dimensional unitary representations of discrete groups e.g. free groups, surface groups
 

Of particular interest are...

I’ll speak about new joint work with Rachel Greenfeld and Marina Iliopoulou in which we address some classical questions concerning the size and structure of integer distance sets. A subset of the Euclidean plane is said to be an integer distance...

In this lecture, we will review recent works regarding  spectral  statistics of the normalized adjacency matrices of random  $d$-regular graphs on $N$ vertices.

Denote their eigenvalues by $\lambda_1=d/\sqrt{d-1}\geq \la_2\geq\la_3\cdots\geq \la_N$...

Since work of Montgomery and Katz-Sarnak, the eigenvalues of random matrices have been used to model the zeroes of the Riemann zeta function and other L-functions. Keating and Snaith extended this to also model the distribution of values of the L...