Alladi Ramakrishnan Hall

Rectangular Billiards and Volumes of Moduli Spaces

Jayadev Athreya

UIUC

In joint work with Eskin and Zorich, we compute quadratic
asymptotics for the number of closed billiard trajectories in right-angled
polygons. The coefficients are ratios of volumes of moduli spaces of
quadratic differentials on the Riemann sphere, which we compute via
combinatorial methods, resolving a conjecture of Kontsevich.