Video Lectures

The stochastic Burgers equation (equivalent to the one-dimensional KPZ equation) is a hyperbolic conservation law with random currents. In applications, one often has to deal with several conservation laws, a little explored case. We discuss...

In several naturally occurring (infinite) point processes, we show that the number (and other statistical properties) of the points inside a finite domain are determined, almost surely, by the point configuration outside the domain. This curious...

I describe recent results on spiked covariance matrices, which model multivariate data containing nontrivial correlations. In principal components analysis, one extracts the leading contribution to the covariance by analysing the top eigenvalues and...

Feynman categories are a new universal categorical framework for generalizing operads, modular operads and twisted modular operads. The latter two appear prominently in Gromov-Witten theory and in string field theory respectively. Feynman categories...

We discuss two random decreasing sequences of continuous functions in two variables, and how they arise as the scaling limit from corners of a (real / complex) Wigner matrix undergoing stochastic evolution. The restriction of the second one to...

We construct a \(\mathrm{KPZ}_t\) line ensemble -- a natural number indexed collection of random continuous curves which satisfies a resampling invariance called the H-Brownian Gibbs property (with \(H(x)=e^x\)) and whose lowest indexed curve is...

Inspired by recent work of Alberts, Khanin and Quastel, we formulate general conditions ensuring that a sequence of multi-linear polynomials of independent random variables (called polynomial chaos expansions) converges to a limiting random variable...

We will discuss interactive coding in the setting where there are n parties attempting to compute a joint function of their inputs using error-prone pairwise communication channels. We will present a general protocol that allows one to achieve only...