Equidistribution of square-tiled surfaces, meanders, and Masur-Veech volumes
Date
26/09/2017
Horaire
14:00 à 15:00
Diffusion
Résume
We show how recent equidistribution results allow to compute approximate values of Masur-Veech volumes of the strata in the moduli spaces of Abelian and quadratic differentials by Monte Carlo method. We also show how similar approach allows to count asymptotical number of meanders of fixed combinatorial type in various settings in all genera. Our formulae are particularly efficient for classical meanders in genus zero. We present a bridge between flat and hyperbolic worlds giving a formula for the Masur-Veech volume of the moduli space of quadratic differentials in the spirit of Mirzakhani-Weil-Peterson volume of the moduli space of curves. Finally we present several conjectures around large genus asymptotics of Masur-Veech volumes.
