Michael Zhao Memorial Student Colloquium

Spring 2021

Each week, the Michael Zhao Memorial Student Colloquium holds 45-minute talks by Columbia mathematics faculty about their own research. The talks are intended for current PhD students in mathematics at Columbia. If you are an undergraduate student or external graduate student and would like to come, please email ggaitsgori@math.columbia.edu or plei@math.columbia.edu.

Seminar Plan

This Spring the Seminar is organized online. It meets on Wednesdays at 4:30p.m. EDT virtually in Zoom, followed by informal gathering through a platform Gather Town.

Zoom link: https://columbiauniversity.zoom.us/j/97602581546

Organizers: Georgy Gaitsgori and Patrick Lei.

Upcoming Seminars

Date and time Speaker Title and abstract
Wednesday, March 10, 4:30p.m. EDT Ioannis Karatzas A trajectorial approach to the gradient flow. Properties of conservative diffusions.

We provide a detailed, probabilistic interpretation for the variational characterization of conservative diffusion as entropic gradient flow. Jordan, Kinderlehrer, and Otto showed in 1998 that, for diffusions of Langevin-Smoluchowski type, the Fokker-Planck probability density flow minimizes the rate of relative entropy dissipation, as measured by the distance traveled in terms of the quadratic Wasserstein metric in the ambient space of configurations. Using a very direct perturbation analysis we obtain novel, stochastic-process versions of such features; these are valid along almost every trajectory of the motion in both the forward and, most transparently, the backward, directions of time. The original results follow then simply by "aggregating", i.e., taking expectations. As a bonus of the analysis, the HWI inequality of Otto and Villani relating relative entropy, Fisher information, and Wasserstein distance, falls in our lap; and with it the celebrated log-Sobolev, Talagrand and Poincare inequalities of functional analysis. (Joint work with Walter Scahchermayer and Bertram Tschiderer, University of Vienna.)
Wednesday, March 24, 4:30p.m. EDT Daniela De Silva TBA

Previous Seminars

Date and time Speaker Title and abstract

Fall 2020

Spring 2020

Fall 2019

Spring 2019

Fall 2018

Spring 2018