Video Lectures

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...

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...

One of the major open problems in complexity theory is proving super-polynomial lower bounds for circuits with logarithmic depth (i.e.,\(P \not\subseteq NC_1\) ). This problem is interesting both because it is tightly related to understanding the...