Video Lectures

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...

In the max cut problem, we are given an n-vertex graph and we are asked what is the maximum fraction of edges "cut" by any partition of the vertices? This problem can be reformulated as an optimization problem over the cut polytope, which has...

Inspired by the symplectic Banach-Mazur distance, proposed by Ostrover and Polterovich in the setting of non-degenerate starshaped domains of Liouville manifolds, we define a distance on the space of contact forms supporting a given contact...

In 1985, Casson introduced an invariant of integer homology 3-spheres by counting SU(2)SU(2)-representations of the fundamental groups. The generalization of Casson invariant by considering Lie groups SU(n) has been long expected, but the original...