Еженедельный семинар Лаборатории: Антон Зорич (Jussieu)

На семинаре выступит Антон Зорич с докладом Flat and hyperbolic enumerative geometry

This talk (based on joint work with V.Delecroix, E.Goujard and P.Zograf) bridges certain aspects of flat and hyperbolic enumerative geometry. We derive from the Kontsevich's count of metric ribbon graphs a formula for the Masur--Veech volume of the moduli space of quadratic differentials in terms of intersection numbers of psi-classes. We show that Mirzakhani's frequencies of simple closed hyperbolic geodesics of different combinatorial types coincide with the frequencies of the corresponding square-tiled surfaces. Using our recent equidistribution results for square-tiled surfaces of fixed combinatorial type we derive applications for the count of meanders on surfaces of arbitrary genus. We conclude with several conjectures concerning the shape of a typical multicurve on a surface of large genus and the shape of a typical square-tiled surface of large genus.