Video Lectures

We study stability problems with respect to families of groups equipped with bi-invariant ultrametrics, that is, metrics satisfying the strong triangle inequality. This property has very strong consequences, and this form of stability behaves very...

In a plethora of random models for constraint satisfaction and statistical inference problems, researchers from different communities have observed computational gaps between what existential or brute-force methods promise, and what known efficient...

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...

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 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...

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...

The question I will address is: How does the holographic principle apply to de Sitter space? 

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

We consider a system of NN particles evolving according to the gradient flow of their Coulomb or Riesz interaction, or a similar conservative flow, and possible added random diffusion. By Riesz interaction, we mean inverse power ss of the distance...

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...