Video Lectures

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...

I will explain that incompressible Navier-Stokes is the wrong equation to describe turbulence in low Mach number molecular fluids because it neglects the effects of thermal noise. There should, in fact, be strong effects of thermal noise throughout...

We present an elementary summary of known results, and open questions, on scaling problems in hydrodynamic turbulence in three dimensions. The goal is to provide some background for the two talks to follow, and summarize Victor Yakhot's theory...

I will explain the construction of a functor from the exact symplectic cobordism category to a totally ordered set, which measures the complexity of the contact structure. Those invariants are derived from a bi-Lie infinity formalism of the rational...

Let λλ be the Liouville function and P(x)P(x) any polynomial that is not a square. An open problem formulated by Chowla and others asks to show that the sequence λ(P(n))λ(P(n)) changes sign infinitely often. We present a solution to this problem for...