Postdoc Talks/Lunch

Date: October 17, 2022

Time: 11:30AM - 12:45PM

Location: BLOC 302

Description: 11:30a.m.
Dr. Tung Nguyen
Title: An introduction to biochemical reaction networks

Abstract: Reaction networks are commonly used to model a variety of physical systems ranging from the microscopic world like cellular processes and chemistry, to the macroscopic world like epidemiology and ecology. When the abundances of the species are high, these systems are often modeled deterministically by a system of ordinary differential equations (ODEs). On the other hand, when the abundances of the species are low, these systems could be modeled stochastically by a continuous-time Markov chain instead. In this talk, I will begin with an introduction to the basic mathematical models of reaction networks, then provide a broad overview of research directions in the field. I will also highlight the fact that many results in the field attempt to establish the connections between the underlying graph structures and the dynamical properties of reaction networks.

Abstract: The problem of biLipschitz embeddability into L1 of the Wasserstein-1 metric on probability measures over a metric space is motivated by both geometric functional analysis and theoretical computer science. We will survey past results in this area and present new ones of the speaker. Based on joint works with Florent Baudier, Thomas Schlumprecht, and David Freeman.

Abstract:We will introduce the finite free multiplicative convolution of two polynomials, and explain how it is related to free probability in the limit. Then we will use it to study the effect of differentiating a sequence of polynomials several times and then looking at the resulting limiting root distribution.