Video Lectures

Determining whether or not a given finitely generated group is permutation stable is in general a difficult problem. In this talk we discuss work of Becker, Lubotzky and Thom which gives, in the case of amenable groups, a necessary and sufficient...

Symplectic implosion was developed to solve the problem that the symplectic cross-section of a Hamiltonian K-space is usually not symplectic, when K is a compact Lie group. The symplectic implosion is a stratified symplectic space, introduced in a...

Smith theory is a type of equivariant localization with respect to a cyclic group of prime order pp, with coefficients in a field of the same characteristic pp. It has been the source of various recent advances in modular representation theory and...

In this lecture I will describe the three concepts appearing in the title and how they connect with each other.

The rigorous calculation of the ground state energy of dilute Bose gases has been a challenging problem since the 1950s. In particular, it is of interest to understand the extent to which the Bogoliubov pairing theory correctly describes the ground...

The talk is about convolution in the setting of geometric representation theory. What are its formal properties? As a starting point, let G be a group and let D(G) be the derived category of constructible sheaves on it. Convolution turns D(G) into a...

The aim of this talk is to show that C*-algebras are useful for studying stability of groups. In particular we will discuss some obstructions for Hilbert-Schmidt stability of groups, obtain a complete characterization of Hilbert-Schmidt stability...

The Stefan problem, dating back to the XIX century, aims to describe the evolution of a solid-liquid interface, typically a block of ice melting in water. A celebrated work of Luis Caffarelli from the 1970's established that the ice-water interface...

Physics inspired mathematics helps us understand the random evolution of Markov processes. For example, the Kolmogorov forward and backward differential equations that govern the dynamics of Markov transition probabilities are analogous to the...

We study the vortex sheet solutions of the Euler equation, which correspond to the tangent discontinuity of the velocity field.

We observe that stationary flows correspond to the Hamiltonian's minimization by the tangent discontinuity density Γ...