## 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.

- 18/05/2022 - Adrien Sauvaget (Université de Cergy Pontoise) - salle 01
- 25/05/2022 - Jayadev Athreya (University of Washington) - salle 201

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.

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.