Samuel Freedman

A non-square-tiled Veech surface has finitely many periodic
points, i.e. points with finite orbit under the whole affine
automorphism group. We first present an algorithm that, when given a
non-square-tiled Veech surface as input, outputs its set of periodic
points. We then describe upcoming work that uses this algorithm to
prove that Prym eigenforms in the minimum stratum in genus 2, 3 and 4
do not have periodic points, except for the fixed points of the Prym
involution.
This work is with Zawad Chowdury, Samuel Everett and Destine Lee.