Counting special trajectories for right-angled billiards and pillowcase covers

Jayadev Athreya (UIUC)

Abstract: In joint work with A. Eskin and A. Zorich, we compute volumes of moduli spaces of meromorphic quadratic differentials on CP, via enumerating pillowcase covers. One motivation comes from understanding the (weak) quadratic asymptotics for counting special trajectories for billiards in polygons whose angles are integer multiples of 90 degrees.