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

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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.