Equidistribution of square-tiled surfaces, meanders, and Masur-Veech volumes | Vidéo | Carmin.tv

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

By Anton Zorich

Appears in collections : 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, Exposés de recherche

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.

Information about the video

Date of recording 31/01/2018
Date of publication 07/02/2018
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19272903
Cite this video ZORICH, Anton (31/01/2018). Equidistribution of square-tiled surfaces, meanders, and Masur-Veech volumes. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19272903
URL https://dx.doi.org/10.24350/CIRM.V.19272903

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Bibliography

Delecroix, V., Goujard, E., Zograf, P., & Zorich, A. (2017). Enumeration of meanders and Masur-Veech volumes. <arXiv:1705.05190> - https://arxiv.org/abs/1705.05190
Delecroix, V., Goujard, E., Zograf, P., & Zorich, A. (2016). Square-tiled surfaces of fixed combinatorial type: equidistribution, counting, volumes of the ambient strata. <arXiv:1612.08374> - https://arxiv.org/abs/1612.08374

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