Video Lectures

Rank 1 transformations are a long studied, flexible class of measure preserving transformations. King proved a variety of deep results about rank 1 rank transformations including: A) A rank 1 transformation’s centralizer is the weak closure of its...

In the '80s, Yau conjectured that every closed Riemannian 3-manifold contains infinitely many smooth minimal hypersurfaces. In this talk, I will present a Yau-type existence result for nonlocal minimal surfaces and discuss how one can recover the...

A closed hypersurface in a contact manifold is convex if it admits a transverse contact vector field. A closed hypersurface is robustly non-convex if it cannot be smoothly approximated by a convex hypersurface. The existence of such hypersurfaces...

I plan to survey the many ways we have today of constructing expanding Cayley graphs of finite groups, and the ideas behind their analysis (some useful beyond that purpose). I want to highlight that despite a comprehensive understanding of achieving...

The India Book Project is a landmark scholarly initiative dedicated to publishing the final three volumes of S. D. Goitein's monumental work on Judeo-Arabic documents from the Cairo Geniza. These documents illuminate the vibrant world of Jewish...

Given a compact hyperbolic surface of fixed topology, we consider its Laplace eigenvalues together with the structure constants for multiplication with respect to a suitable orthonormal basis of Laplace eigenforms. These numbers obey algebraic...

We develop the spectral analysis of the Jacobi operator on the interfaces of soap-bubble clusters. By Plateau's laws, these always meet in threes at $120^{\circ}$-angles, and thus naturally interact via 3 linearly independent "conformal" boundary...

I will discuss the quantum resource known as magic and its analysis in many-fermion systems such as the Sachdev-Ye-Kitaev model. I will show that the SYK calculation of magic can be quantitatively modeled with a gravity calculation involving...

Singularities are local properties of algebraic varieties. For example, the solution set of a polynomial in several variables such as $y^2=x^3$ has a singularity at the origin $(0,0)$. In algebra, one often studies singularities through the quotient...

We define and study an extension of the notion of the VC-dimension of a hypergraph and apply it to establish a Tverberg type theorem for unions of convex sets. We also prove a new Radon type theorem for unions of convex sets, settling an open...