Géométrie et dynamique dans les espaces de modules

Séminaire Mensuel

Séminaire - Mai

Le séminaire aura lieu deux mercredis ce mois (exceptionnellement) de 14h à 15h à l'Institut Henri Poincaré à Paris.  Pour télécharger le programme du mois: mai.pdf.

  • 18/05/2022Adrien Sauvaget (Université de Cergy Pontoise)  -  salle 01

  • Titre: Integrals on DR-cycles and strata of differentials.

    Resumé: I will present how to integrate a single psi-class on generalized DR-cycle and how this produce formulas for integrals of a psi-class on strata of differentials. I will also present spin refinements of these formulas and some applications of these results. Based on j.w. with M. Costantini and J. Schmitt.

  • 25/05/2022Jayadev Athreya (University of Washington)  -  salle 201

  • Titre: Counting pairs of saddle connections.

    Resumé: We show that for almost every translation surface the number of pairs of saddle connections with bounded virtual area has asymptotic growth like \(c{R}^2\) where the constant \(c\) depends only on the area and the connected component of the stratum. The proof techniques combine classical results for counting saddle connections with the crucial result that the Siegel-Veech transform is in \({L}^2\). In order to capture information about pairs of saddle connections, we consider pairs with bounded virtual area since the set of such pairs can be approximated by a fibered set which is equivariant under geodesic flow. In the case of lattice surfaces, small virtual area is equivalent to counting parallel pairs of saddle connections, which also have a quadratic growth of \(c{R}^2\) where \(c\) depends in this case on the given lattice surface. This is joint work with Samantha Fairchild and Howard Masur.