Veech surfaces and simple closed curves

Robert Tang (Oklahoma)

Abstract

Veech surfaces are a class of "very symmetric" flat surfaces possessing dynamical properties akin to flat tori. The first interesting examples were discovered by Veech in the context of billiard trajectories on rational polygons. In this talk, I will introduce some basic notions, and state some characterisations of Veech surfaces due to Smillie-Weiss and Vorobets. Our main result is a new characterisation of Veech surfaces using lengths of simple closed curves. This is joint work with Max Forester and Jing Tao.