Video Lectures

Motivated by the study of billiards in polyhedra, we study linear flows in a family of singular flat 3-manifolds which we call translation prisms. Using ideas of Furstenberg, and Veech, we connect results about weak mixing properties of flows on...

Several recent groundbreaking results in geometric measure theory, homogeneous dynamics and number theory ultimately rely on a key result of Bourgain known as Bourgain's Projection Theorem (of course, each of these results require many other tools...

I will start by reviewing various Hodge-theoretic invariants of complex singularities. After that, I will discuss how to study such singularities using methods of positive characteristic such as Cartier operators. This is based on joint work with...

This talk will be about two related results, one in complexity theory and one in learning.

On the learning side, we investigate the sample complexity of smooth boosters - These are boosting algorithms that do not place too much weight on any given...

Multiple polylogarithms appear to be central to many seemingly unrelated areas of mathematics, including the volumes of hyperbolic polytopes, scissors congruence, algebraic K-theory, and special values of zeta functions. Despite this broad network...

The talk will be on recent progress in a series of joint papers with Filip Živanović, about a large class of non-compact symplectic manifolds, which includes semiprojective toric manifolds, quiver varieties, and conical symplectic resolutions of...

I will give an overview of recent progress in random multiplicative functions (random models for multiplicative functions) and their connection to the study of the Fyodorov-Hiary-Keating conjecture and Polya's question on nonnegative character sums...

Gas-rich environments are ubiquitous in various scales, from protoplanetary disks to star clusters and galaxies. Dynamics in gas-rich environments are substantially different and give rise to unique astrophysical phenomena, along with enhancing the...

The long-standing F-Conjecture asserts that there is a very simple description for the closed cone of effective curves on the moduli space M_{g,n}\bar of stable n-pointed curves of genus g as being determined by a finite collection of so-called F...

In 1984, Ryan showed that any smooth Schubert variety in type A is an iterated fiber-bundle of Grassmannian varieties. Later, Haiman calculated the generating function for the number of smooth permutations (equivalently smooth Schubert varieties) of...