Max Weinreich : Algebraic billiards and dynamical degrees

Posted by Nicole Looper , part of the Unlikely Intersections Seminar.

At

Nov. 1, 2023, 3 p.m.

In

1227 SEO

Abstract

Billiards is a dynamical system that models the behavior of a point particle bouncing around some region. If the region is a plane region bounded by an algebraic curve, then we can use tools from algebraic geometry to study the billiards map in that region. In this talk, we explain how to view billiards as a complex algebraic correspondence, and we investigate its dynamical degree, a difficult-to-compute invariant that measures the asymptotic growth rate of the degrees of the iterates. We show that the dynamical degree of billiards in a general plane curve of degree $d$ is approximately $2d^2$.