Video Lectures

After a brief review of various classical connections between problems of polynomial zero localization, continued fractions, and matrix theory, I will show a few ways to generalize these classical techniques to get new results about some interesting...

In this talk, I will describe a new framework for approximately solving flow problems in capacitated, undirected graphs, and I will apply it to find approximately maximum s-t flows in almost-linear time, improving on the best previous bound of \(...

The Fukaya category of a fibration with singularities \(W: M \to C\), or Fukaya-Seidel category, enlarges the Fukaya category of \(M\) by including certain non-compact Lagrangians and asymmetric perturbations at infinity involving \(W\); objects...

According to first principle quantum mechanics, the evolution of N fermions (particles with antisymmetric wave function) is governed by the many body Schroedinger equation. We are interested, in particular, in the evolution in the mean field regime...

I will continue last week's discussion of this model, this time giving sketches of proofs of some of the theorems. No technical background is necessary for this lecture, but for motivation and background it is good to consult the Tue Feb 11 talk...

We consider an harmonic chain perturbed by an energy conserving noise and show that after a space-time rescaling the energy-energy correlation function is given by the solution of a skew-fractional heat equation with exponent 3/4.

One of the most studied objects in mathematics is the modular curve, which is the quotient of hyperbolic 2-space by the action of \(\mathrm{SL}_2(\mathbb Z)\). It is naturally the home of modular forms, but it also admits an algebraic structure. The...