3/4-Fractional superdiffusion in a system of harmonic oscillators perturbed by a conservative noise

Cédric Bernardin
Université Nice Sophia Antipolis
February 18, 2014
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.

Hartree-Fock dynamics for weakly interacting fermions

Benjamin Schlein
University of Bonn
February 19, 2014
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, characterized by a large number of weak collisions among the particles. For fermions, the mean field regime is naturally linked with a semiclassical limit. Asymptotically, the many body Schroedinger evolution can therefore be described by the classical Vlasov equation.

A criterion for generating Fukaya categories of fibrations

Sheel Ganatra
Stanford University
February 21, 2014
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 include Lefschetz thimbles if \(W\) is a Lefschetz fibration. I will recall this category and then explain a criterion, in the spirit of work of Abouzaid and Abouzaid-Fukaya-Oh-Ohta-Ono, for when a finite collection of Lagrangians split-generates such a fibration.

An Almost-Linear-Time Algorithm for Approximate Max Flow in Undirected Graphs, and its Multicommodity Generalizations

Jonathan Kelner
Massachusetts Institute of Technology
February 24, 2014
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 \(\tilde O(mn^{1/3})\).

In describing the algorithm, I will discuss several new technical tools that may be of independent interest:

Zeros of polynomials via matrix theory and continued fractions

Olga Holtz
University of California, Berkeley; Member, School of Mathematics
February 24, 2014
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 polynomials and entire functions.