Siegel-Veech constants and Masur-Veech volumes: Connection to Intersection theory

• Applicant: Professor Dr. Martin Möller
• Subject Area: Mathematics
• Term: from 2015 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 275218485

Siegel-Veech constants measure the asymptotic number of closed trajectories up to a given length bound on a billiard table. They are closely related to ratios of volumes on the moduli spaces of flat surfaces, the Masur-Veech volumes. While previously those Masur-Veech volumes have been computed through asymptotics of counting torus covers, connections to intersection theory on moduli spaces recently established provide a new approach that we plan to extend to quadratic differentials and more generally to all affine invariant manifolds.

• DFG Programme: Research Grants
• International Connection: France, Netherlands, USA
• Cooperation Partners: Professor Dawei Chen; Professorin Dr. Elise Goujard; Adrien Sauvaget