Video Lectures

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...

In recent decades, physicists and astronomers have discovered two beautiful Standard Models, one for the quantum world of extremely short distances, and one for the universe as a whole. Both models have had spectacular success, but there are also...

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...

I will present some recent applications of symplectic geometry to the restricted three body problem. More specifically, I will discuss how Gromov's original study of pseudoholomorphic curves in the complex projective plane has led to the...

We will outline the proof that gives a positive solution of to Weaver's conjecture \(KS_2\). That is, we will show that any isotropic collection of vectors whose outer products sum to twice the identity can be partitioned into two parts such that...

I will discuss the proof by Yang Kang and myself of diffusion for the Markov Anderson model, in which the potential is allowed to fluctuate in time as a Markov process. However, I want to highlight the method of the proof more than the result itself...