Video Lectures

 q-deformed Virasoro and W-algebras were defined a quarter century ago with the aim of furthering our understanding of two-dimensional integrable and conformal field theories, while also developing the representation theory of so-called quantum...

In various areas of mathematics there exist "big fiber theorems", these are theorems of the following type: "For any map in a certain class, there exists a 'big' fiber", where the class of maps and the notion of size changes from case to case.

Understanding of the role magnetic field in astrophysical environments is essential for many brunches of astrophysical research. The knowledge of magnetic field and polarized radiation that this field induces is important for the ongoing search for...

After surveying some important consequences of the property of bounded generation (BG) dealing with SS-rigidity, the congruence subgroup problem, etc., we will focus on examples of boundedly generated groups. We will prove that every unimodular (n×n...

A fundamental problem in the theory of compressible fluid is to provide a precise description of shock formation and development from smooth initial data. In this talk, I will present recent work in collaboration with Drivas, Shkoller and Vicol on...

A random point process is said to be determinantal if finite subset probabilities correspond to principal minors of some matrix. Determinantal point processes (DPPs) appear in a wide variety of settings, from random matrix theory to combinatorics...

30 years ago I proved that any tight contact structure on the 3-sphere is diffeomorphic to the standard one. I also optimistically claimed at the same paper that similar methods could be used to prove a multi-parametric version: the space of tight...