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H 1 Equidistribution of square-tiled surfaces, meanders, and Masur-Veech volumes

Auteurs : Zorich, Anton (Auteur de la Conférence)
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 :
    05Axx - Enumerative combinatorics
    05C30 - Enumeration in graph theory
    32G15 - Moduli of Riemann surfaces, Teichmüller theory

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 07/02/2018
      Date de captation : 31/01/2018
      Collection : Research talks ; Combinatorics ; Dynamical Systems and Ordinary Differential Equations ; Topology
      Format : MP4
      Durée : 01:06:16
      Domaine : Topology ; Combinatorics ; Dynamical Systems & ODE
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2018-01-31_Zorich.mp4

    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 quantique
    Organisateurs 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

    Citation Data

    DOI : 10.24350/CIRM.V.19272903
    Cite this video as: 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

    Voir aussi


    1. Delecroix, V., Goujard, E., Zograf, P., & Zorich, A. (2017). Enumeration of meanders and Masur-Veech volumes. - https://arxiv.org/abs/1705.05190

    2. Delecroix, V., Goujard, E., Zograf, P., & Zorich, A. (2016). Square-tiled surfaces of fixed combinatorial type: equidistribution, counting, volumes of the ambient strata. - https://arxiv.org/abs/1612.08374

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