Department of Mathematics Calendar

Back to Listing

The Department of Mathematics Calendar has moved to Webtools. Anyone may submit an event by clicking the "+" button (upper right). Note: the Sponsor field is required. Just type "n/a"

All events will be reviewed before acceptance. Please email Shelby Koehne if you have any questions about submitting an event.

Note: you may search past and future events by clicking on the magnifying glass icon on the main Calendar page.

For an archive of past events: https://math.illinois.edu/research/seminars-department-calendar

Mathematical Biology Seminar: Flux in small noise dynamics: negative resistance and persistence

Event Type
Lecture
Sponsor
n/a
Virtual
wifi event
Date
Oct 14, 2021   1:00 pm  
Speaker
Matthew Kvalheim
Contact
Zoi Rapti
E-Mail
zrapti@illinois.edu
Views
5

Abstract: Many biological and physical systems are well-modeled by Brownian particles subject to gradient dynamics plus noise. Important for many applications is the net steady-state particle current or "flux" enabled by the noise and an additional driving force, but this flux is rarely computable analytically. Motivated by this, I will describe joint work with Yuliy Baryshnikov investigating the steady-state flux of nondegenerate diffusion processes on compact manifolds. Such a flux is associated to each one-dimensional real cohomology class and is equivalent to an asymptotic winding rate of trajectories. When the deterministic part of the dynamics is "gradient-like" in a certain sense, I will describe a graph-theoretic formula for the small-noise asymptotics of the flux (in the sense of large deviations). When additionally the deterministic part is locally gradient and close to a generic global gradient, there is a natural flux for which the graph-theoretic formula becomes Morse-theoretic and admits a description in terms of persistent homology. As an application, I will explain the paradoxical "negative resistance" phenomenon in Brownian transport discovered by Cecchi and Magnasco (1996).

link for robots only