# Video Lectures

We consider a class of interacting particle systems with two types, A and B which perform independent random walks at different speeds. Type A particles turn into type B when they meet another type B particle. This class of systems includes models...

Most of the visible matter in the Universe is a plasma, that is a dilute gas of ions, electrons, and neutral atoms. In many circumstances, the dynamics of this plasma can be modeled in the continuum limit, using the equations of fluid mechanics...

### Optimal Mixing of Glauber Dynamics: Entropy Factorization via High-Dimensional Expansion

We consider the Glauber dynamics (also called Gibbs sampling) for sampling from a discrete distribution in high-dimensional space (e.g., selecting a uniformly random legal coloring or independent set in a given graph, or selecting a "typical" state...

Gross and Siebert have recently proposed an "intrinsic" programme for studying mirror symmetry. In this talk, we will discuss a symplectic interpretation of some of their ideas in the setting of affine log Calabi-Yau varieties. Namely, we describe...

Given a K3 surface XX over a number field KK, we prove that the set of primes of KK where the geometric Picard rank jumps is infinite, assuming that XX has everywhere potentially good reduction. This result is formulated in the general framework of...

A theorem of Bernstein identifies the center of the affine Hecke algebra of a reductive group GG with the Grothendieck ring of the tensor category of representations of the dual group G?G?. Gaitsgory constructed a functor which categrorifies this...

Some years ago, I proved with Shulman and Sørensen that precisely 12 of the 17 wallpaper groups are matricially stable in the operator norm. We did so as part of a general investigation of when group C?C?-algebras have the semiprojectivity and weak...

Expander graphs are graphs which simultaneously are both sparse and highly connected. The theory of expander graphs received a lot of attention in the past half a century, from both computer science and mathematics. In recent years, a new theory of...

Valiant (1980) showed that general arithmetic circuits with negation can be exponentially more powerful than monotone ones. We give the first qualitative improvement to this classical result: we construct a family of polynomials P-n in n variables...