23/02/2022, 16:00 — 17:00 — Online
Krzysztof Burdzy, University of Washington
From billiards to PDEs via white noise
I will start by presenting a number of known published rigorous upper and lower bounds for the number of collisions of a finite number of billiard balls in free space (i.e., a billiard table with no walls). The known bounds are not sharp. Those questions inspired a model with "pinned billiard balls" that have "velocities" and collide with each other but do not move. The evolution of pseudo-velocities seems to be well represented by modulated white noise. The parameters of white noise, the mean and standard deviation, are deterministic functions of space and time. They satisfy a simple system of PDEs with complicated boundary conditions.
Joint work with J. Athreya, M. Duarte, J. Hoskins, S. Steinerberger and J. Sylvester.
