Video Lectures

A fundamental problem in the theory of compressible fluid is to provide a precise description of shock formation and development from smooth initial data. In this talk, I will present recent work in collaboration with Drivas, Shkoller and Vicol on...

A random point process is said to be determinantal if finite subset probabilities correspond to principal minors of some matrix. Determinantal point processes (DPPs) appear in a wide variety of settings, from random matrix theory to combinatorics...

30 years ago I proved that any tight contact structure on the 3-sphere is diffeomorphic to the standard one. I also optimistically claimed at the same paper that similar methods could be used to prove a multi-parametric version: the space of tight...

We study the Lyapunov exponent in disordered quantum field theories. Generically the Lyapunov exponent can only be computed in isolated CFTs, and little is known about the way in which chaos grows as we deform the theory away from weak coupling. In...

What does the spectrum of a random matrix look like when we make no assumption whatsoever about the covariance pattern of its entries?  It may appear hopeless that anything useful can be said at this level of generality. Nonetheless, a widely used...

We study CM cycles on Kuga-Sato varieties over X(N) via theta lifting and relative trace formula. Our first result is the modularity of CM cycles, in the sense that the Hecke modules they generate are semisimple whose irreducible components are...

In this talk I will discuss two undetected populations of black holes. In the faraway Universe, the first lensed z > 6 quasar (J0439+1634) was recently discovered. We predicted that the observed population of quasars should contain many mildly...