Probability and Mathematical Physics Seminar

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Branching Brownian motion and the Road-Field Model

Speaker: Nicholas Cook, Duke University

Location: Warren Weaver Hall 1302

Date: Friday, October 13, 2023, 11:10 a.m.

Synopsis:

The Fisher-KPP equation was introduced in 1937 to model the spread of an advantageous gene through a spatially distributed population. Remarkably precise information on the traveling front has been obtained via a connection with branching Brownian motion, beginning with works of McKean and Bramson in the 70s. I will discuss an extension of this probabilistic approach to the Road-Field Model: a reaction-diffusion PDE system introduced by H. Berestycki et al. to describe enhancement of biological invasions by a line of fast diffusion, such as a river or a road. Based on joint work with Amir Dembo.