Video Lectures

How many arithmetic operations does it take to multiply two square matrices? This question has captured the imagination of computer scientists ever since Strassen showed in 1969 that \(O(n^{2.81})\) operations suffice. We survey the classical theory...

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...