Sam Freedman

Periodic Points on Veech Surfaces

In this talk, we will study the dynamics of automorphisms acting on highly symmetric translation surfaces known as Veech surfaces. Specifically, we will focus on the periodic points — those with a finite orbit under the full automorphism group. While it is known that this set is finite for non-arithmetic Veech surfaces, applications often require an explicit determination of these periodic points. We will classify periodic points for minimal Prym eigenforms, a specific class of primitive Veech surfaces, in genus 2, 3, and 4.