Video Lectures

I present some new dispersive estimates for Schroedinger's equation with a time-dependent potential, together with applications.

For a set of polynomials F, we define their bilinear complexity as the smallest k so that F lies in an ideal generated by k bilinear polynomials. The main open problem is to estimate the bilinear complexity of the single polynomial $\sum_{i,j}x_i^2...

We will give an overview of this system, which has been at the center of recent algorithmic and proof complexity developments. We will give the definitions of the system (as a proof system for polynomial inequalities, and as an SDP-based algorithm)...

We consider Galois cohomology groups over function fields F of curves that are defined over a complete discretely valued field.
Motivated by work of Kato and others for n=3, we show that local-global principles hold for
$H^n(F, Z/mZ(n-1))$ for all...

This is from joint works with D. Knopf and I. M. Sigal. In this talk I will present a new strategy in studying neckpinching of mean curvature flow. Different from previous results, we do not use backward heat kernel, entropy estimates or subsequent...