Seminars Sorted by Series

I will describe a program aimed at understanding numerics of representations of quantized symplectic resolutions in positive characteristic. A key ingredient is a generalization of the action of the affine braid group on the derived category of...

According to Langlands’ conjectures, algebraic automorphic forms should be parametrized by global Galois representations, and smooth representations of $p$-adic groups should be parametrized by local Galois representations. These parametrizations...

A symplectic singularity has a natural stratification by Poisson leaves, which are symplectic, hence even-dimensional.  Perverse sheaves constructible with respect to this stratification are semisimple if the coefficients are in characteristic zero...

Let G be a semisimple group over an algebraically closed field of large characteristic. There are two important types of rational representations of G: the Weyl modules and the simple modules. We will explain how to go from the first type to the...

The study of totally positive matrices, i.e., matrices with positive minors, dates back to 1930s. The theory was generalised by Lusztig to arbitrary split reductive groups using canonical bases, and has significant impacts on the theory of cluster...

The talk is based on a joint work with Pablo Boixeda Alvarez. We study equivariant Borel-Moore homology of certain affine Springer fibers and relate them to global sections of suitable vector bundles arising from Procesi bundles on Q-factorial...

In 1997, Kuperberg gave a generators-and-relations presentation of the monoidal category Fund, whose objects are tensor products of fundamental representations, for all rank 2 lie algebras. The general case has been an open problem since. It was...

Abstract: In 2000, Arnaud Beauville introduced the notion of symplectic singularities and raised the question of classifying isolated symplectic singularities with trivial local fundamental group: the latter condition is meant to avoid the numerous...

What can one say about the fields of values of irreducible complex characters $\chi$ of a given finite group $G$? In particular when $G$ is a finite (quasi)simple group? What about the ``McKay situation'', i.e. when the degree of $\chi$ is coprime...

I will explain the construction of an action of the Hecke category on the principal block of representations of a connected reductive algebraic group over an algebraically closed field of positive characteristic, obtained in joint work with Roman...

Using the arithmetics of quantum numbers we construct some “approximations” of tilting modules for reductive algebraic groups that might be useful for understanding the generational patterns of tilting characters conjectured by Lusztig and...

Let $G$ be a complex reductive group, $G^*$ its dual Poisson-Lie group, and $g$ the Lie algebra of $G$. $G$-valued Stokes phenomena were exploited by P. Boalch to linearise the Poisson structure on $G^*$. I will explain how $Ug$-valued Stokes...

The Langlands program is a far-reaching collection of conjectures that relate different areas of mathematics including number theory and representation theory. A fundamental problem on the representation theory side of the local Langlands program is...

In joint work with Andy Manion, we required a generalization of the tensor product of 2-representations in order to reconstruct the 2-dimensional part of Lipshitz-Oszvath-Szabo’s bordered Heegaard-Floer theory. I will discuss this and possible...

Given a maximal torus $T$ of a connected reductive group $G$ over a local field $F$, there does not exist a canonical embedding of the L-group of $T$ into the L-group of $G$. Generalizing work of Adams and Vogan in the case $F=R$, we will construct...

In an ongoing project of D. Ben-Zvi, Y. Sakellaridis and A. Venkatesh, the authors propose a conjectural generalization of the derived Satake equivalence for complex reductive groups to spherical varieties. I will describe a program aimed at...

The study of totally positive matrices, i.e., matrices with positive minors, dates back to 1930s. The theory was generalised by Lusztig to arbitrary split reductive groups using canonical bases, and has significant impacts on the theory of cluster...

Let $g$ be a semisimple Lie algebra. The affine W-algebra associated to $g$ is a topological algebra which quantizes the algebraic loop space of the Kostant slice. It is constructed as a quantum Hamiltonian (alias quantum Drinfeld--Sokolov)...