Unlikely Intersections Seminar
Max Weinreich
Harvard University
Algebraic billiards and dynamical degrees
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 $2d^2$.
Wednesday November 1, 2023 at 3:00 PM in 1227 SEO