EnglishEquidistribution of square-tiled surfaces, meanders, and Masur-Veech volumes
Multi angle
Auteurs : Zorich, Anton (Auteur de la Conférence)
CIRM (Editeur )
05Axx - Enumerative combinatorics
05C30 - Enumeration in graph theory
32G15 - Moduli of Riemann surfaces, Teichmüller theory
CIRM (Editeur )
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Résumé :
We show how recent results of the authors on equidistribution of square-tiled surfaces of given combinatorial type allow to compute approximate values of Masur-Veech volumes of the strata in the moduli spaces of Abelian and quadratic differentials by Monte Carlo method.
We also show how similar approach allows to count asymptotical number of meanders of fixed combinatorial type in various settings in all genera. Our formulae are particularly efficient for classical meanders in genus zero.
We construct a bridge between flat and hyperbolic worlds giving a formula for the Masur-Veech volume of the moduli space of quadratic differentials in terms of intersection numbers of $\mathcal{M}_{g,n}$ (in the spirit of Mirzakhani's formula for Weil-Peterson volume of the moduli space of pointed curves).
Joint work with V. Delecroix, E. Goujard, P. Zograf.
Codes MSC : We also show how similar approach allows to count asymptotical number of meanders of fixed combinatorial type in various settings in all genera. Our formulae are particularly efficient for classical meanders in genus zero.
We construct a bridge between flat and hyperbolic worlds giving a formula for the Masur-Veech volume of the moduli space of quadratic differentials in terms of intersection numbers of $\mathcal{M}_{g,n}$ (in the spirit of Mirzakhani's formula for Weil-Peterson volume of the moduli space of pointed curves).
Joint work with V. Delecroix, E. Goujard, P. Zograf.
05Axx - Enumerative combinatorics
05C30 - Enumeration in graph theory
32G15 - Moduli of Riemann surfaces, Teichmüller theory
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Informations sur la Vidéo
Langue : AnglaisDate de publication : 07/02/2018 Date de captation : 31/01/2018 Sous collection : Research talks arXiv category : Geometric Topology ; Algebraic Geometry ; Combinatorics ; Dynamical Systems Domaine : Topology ; Combinatorics ; Dynamical Systems & ODE Format : MP4 (.mp4) - HD Durée : 01:06:16 Audience : Researchers Download : https://videos.cirm-math.fr/2018-01-31_Zorich.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Representation spaces, Teichmüller theory, and their relationship with 3-manifolds from the classical and quantum viewpoints / Espaces de représentations, théorie de Teichmüller et leur rapport avec les 3-variétés d'un point de vue classique et quantiqueOrganisateurs de la rencontre : Boileau, Michel ; Kitano, Teruaki ; Morifuji, Takayuki ; Paoluzzi, Luisa Dates : 29/01/2018 - 02/02/2018 Année de la rencontre : 2018 URL Congrès : https://conferences.cirm-math.fr/1891.html
Données de citation
DOI : 10.24350/CIRM.V.19272903Citer cette vidéo: Zorich, Anton (2018). Equidistribution of square-tiled surfaces, meanders, and Masur-Veech volumes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19272903 URI : http://dx.doi.org/10.24350/CIRM.V.19272903 |
Bibliographie
- Delecroix, V., Goujard, E., Zograf, P., & Zorich, A. (2017). Enumeration of meanders and Masur-Veech volumes.
- Delecroix, V., Goujard, E., Zograf, P., & Zorich, A. (2016). Square-tiled surfaces of fixed combinatorial type: equidistribution, counting, volumes of the ambient strata.
