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Equidistribution of square-tiled surfaces, meanders, and Masur-Veech volumes
Multi angle
Authors : Zorich, Anton (Author of the conference)
CIRM (Publisher )
05Axx - Enumerative combinatorics
05C30 - Enumeration in graph theory
32G15 - Moduli of Riemann surfaces, Teichmüller theory
CIRM (Publisher )
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Abstract :
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.
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 07/02/2018 Conference Date : 31/01/2018 Subseries : Research talks arXiv category : Geometric Topology ; Algebraic Geometry ; Combinatorics ; Dynamical Systems Mathematical Area(s) : Topology ; Combinatorics ; Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 01:06:16 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2018-01-31_Zorich.mp4 
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Information on the Event
Event Title : 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 quantiqueEvent Organizers : Boileau, Michel ; Kitano, Teruaki ; Morifuji, Takayuki ; Paoluzzi, Luisa Dates : 29/01/2018 - 02/02/2018 Event Year : 2018 Event URL : https://conferences.cirm-math.fr/1891.html
Citation Data
DOI : 10.24350/CIRM.V.19272903Cite 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 |
See Also
- [Post-edited] Differential equation for the Reidemeister torsion / Author of the conference Marché, Julien.
- [Multi angle] L-space knots in twist families and satellite L-space knots / Author of the conference Motegi, Kimihiko.
- [Multi angle] Finite type invariants of knots in homology 3-spheres / Author of the conference Moussard, Delphine.
Bibliography
- 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.
