Séminaire - Mai
Le séminaire aura lieu un mercredi par mois de 14h à 15h à l'Institut Henri Poincaré à Paris. Pour télécharger l'affiche du mois: mai.pdf.
- 15/05/2019 - Gaëtan Borot (Max Planck Institute for Mathematics) - salle 05
Titre:
Masur-Veech volumes from topological recursion
Resumé: Statistics
of the simple length spectrum of bordered hyperbolic surfaces define
functions on the moduli space. Andersen, Orantin and the speaker showed
recently that they satisfy a recursion on the Euler characteristic,
which implies a topological recursion for their averages over the
Weil-Petersson measure. This can be seen as a generalization of
Mirzakhani's identity and her proof of a topological recursion for the
Weil-Petersson voulmes.
We show how this result implies topological recursion (here taking the
form of Virasoro constraints) for the Weil-Petersson averages of the
asymptotic growth of the number of long curves. By invoking the
relation between Weil-Petersson measure on the Teichmuller space,
Thurston measure on the space of measured laminations, and Masur-Veech
measure on the space of quadratic differentials, this gives a recursion
to compute polynomials \(P_{g,n}(L_1,...,L_n)\) whose constant term are
the Masur-Veech volumes. This retrieve and generalizes a result of
Delecroix et al. obtained via different (combinatorial) methods.
If time permits, I will present some conjectural formulas for
Masur-Veech volumes and area Siegel-Veech constants in low genus for
any number of punctures.
This is based on ongoing joint work with Severin Charbonnier, Vincent
Delecroix, Alessandro Giacchetto, Danilo Lewanski and Campbell Wheeler.