Séminaire - Novembre
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: novembre.pdf.
- 13/11/2019 - Eduard Duryev (Université Paris 7) - salle 421
Titre:
Masur-Veech volumes and intersection numbers on moduli spaces.
Resumé:
In this talk I will present a way of computing Masur-Veech volumes of
certain strata of quadratic differentials that uses intersection
numbers on the moduli spaces. This is a joint project with Elise
Goujard.
Kontsevich polynomial \(N_{g,n}(b_1,…,b_n)\) enumerates trivalent metric ribbon graphs of genus g with faces of lengths \(b_1,…, b_n\). Kontsevich showed that the coefficients of the top degree part of the polynomial are intersection numbers of psi classes on \(M_{g,n}\), which allows to efficiently compute numbers of such graphs. Recently Delecroix-Goujard-Zograf-Zorich found a formula for the volume of principal strata \(Q(1^k,-1^l)\) that involves a sum over stable graphs and Kontsevich polynomials. The goal of our project is to find such formula for any stratum with zeroes of odd orders. I will introduce a generalization of Kontsevich polynomial that enumerates trivalent metric ribbon graphs with any prescribed odd valencies of vertices and show how to compute volumes of \(Q(3,1^k,-1^l)\) and \(Q(5,1^k,-1^l)\).
Kontsevich polynomial \(N_{g,n}(b_1,…,b_n)\) enumerates trivalent metric ribbon graphs of genus g with faces of lengths \(b_1,…, b_n\). Kontsevich showed that the coefficients of the top degree part of the polynomial are intersection numbers of psi classes on \(M_{g,n}\), which allows to efficiently compute numbers of such graphs. Recently Delecroix-Goujard-Zograf-Zorich found a formula for the volume of principal strata \(Q(1^k,-1^l)\) that involves a sum over stable graphs and Kontsevich polynomials. The goal of our project is to find such formula for any stratum with zeroes of odd orders. I will introduce a generalization of Kontsevich polynomial that enumerates trivalent metric ribbon graphs with any prescribed odd valencies of vertices and show how to compute volumes of \(Q(3,1^k,-1^l)\) and \(Q(5,1^k,-1^l)\).