Perlen-Kolloquium: Corinna Ulcigrai (University of Bristol)

Mathematical billiards and flows on surfaces

A mathematical billiard consists of a planar domain where a ball travels without friction bouncing elastically at the boundary. Motivated by problems in physics and in contrast to an actual game of billiards, mathematicians study ball trajectories that never hits a pocket and rebounds infinitely off the table walls.  We will explain how, when the table is a (rational) polygon, one can reduce the problem to the study of surface flows. We will also present some recent results on coding of billiards in regular polygons and chaotic properties of area preserving flows on surfaces.

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