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Random hyperbolic surfaces
Multi angle
Authors : Budd, Timothy (Author of the conference)
CIRM (Publisher )
05C80 - Random graphs
30F60 - Teichmüller theory
82B41 - Random walks, random surfaces, lattice animals, etc.
CIRM (Publisher )
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Abstract :
Going back at least to the works of Witten and Kontsevich, it is known that (symplectic or Weil-Petersson) volumes of moduli spaces of Riemann surfaces share many features with the enumeration of maps. It is therefore natural to expect that the theory of random hyperbolic metrics sampled according to the Weil-Petersson measure on, say, punctured spheres is closely related to the theory of random planar maps. I will highlight some similarities and show that tree bijections, which are ubiquitous in the study of random planar maps, have analogues for hyperbolic surfaces. As an application, jointly with Nicolas Curien, we show that these random hyperbolic surfaces with properly rescaled metric admit a scaling limit towards the Brownian sphere when the number of punctures increases.
Keywords : Weil-Petersson volumes; Brownian sphere; random trees
MSC Codes : Keywords : Weil-Petersson volumes; Brownian sphere; random trees
05C80 - Random graphs
30F60 - Teichmüller theory
82B41 - Random walks, random surfaces, lattice animals, etc.
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 04/02/2022 Conference Date : 18/01/2022 Subseries : Research talks arXiv category : Probability ; Geometric Topology ; Mathematical Physics Mathematical Area(s) : Mathematical Physics ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:54:52 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2022-01-18_Budd.mp4 
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Information on the Event
Event Title : Random Geometry / Géométrie aléatoireEvent Organizers : Curien, Nicolas ; Goldschmidt, Christina ; Le Gall, Jean-François ; Miermont, Grégory ; Rhodes, Rémi Dates : 17/01/2022 - 21/01/2022 Event Year : 2022 Event URL : https://conferences.cirm-math.fr/2528.html
Citation Data
DOI : 10.24350/CIRM.V.19876403Cite this video as: Budd, Timothy (2022). Random hyperbolic surfaces. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19876403 URI : http://dx.doi.org/10.24350/CIRM.V.19876403 |
See Also
- [Multi angle] Some questions on the Brownian Map motivated by its higher-genus analogues / Author of the conference Chapuy, Guillaume.
- [Multi angle] Height coupled trees / Author of the conference Ünel, Meltem.
- [Multi angle] Growing maps face by face / Author of the conference Caraceni, Alessandra.
- [Multi angle] Resolution of Liouville CFT : Segal axioms and bootstrap / Author of the conference Guillarmou, Colin.
- [Multi angle] Conformal bootstrap in Liouville theory / Author of the conference Vargas, Vincent.
- [Multi angle] Maps, Hurwitz numbers and formulas for free probability at all genera / Author of the conference Borot, Gaëtan.
- [Multi angle] Generalised Kontsevich graphs, topological recursion and r-spin intersection numbers / Author of the conference Garcia-Failde, Elba.
- [Multi angle] Multicritical Schur measures / Author of the conference Bouttier, Jérémie.
- [Multi angle] The scaling limit of random planar maps with large faces / Author of the conference Riera, Armand.
- [Multi angle] Unicellular maps vs hyperbolic surfaces in high genus / Author of the conference Louf, Baptiste.
- [Multi angle] Bijections for maps on non-oriented surfaces / Author of the conference Dołęga, Maciej.
- [Multi angle] Nonbijective scaling limit of maps via restriction / Author of the conference Bettinelli, Jérémie.
- [Multi angle] The skew Brownian permuton: a new universal limit for random constrained permutations and its connections with Liouville quantum gravity / Author of the conference Borga, Jacopo.
- [Multi angle] Geometry of the sign clusters in the Infinite Ising-weighted triangulation / Author of the conference Albenque, Marie.
Bibliography
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