English
Combinatorial maps and hyperbolic surfaces in high genus
Multi angle
Auteurs : Louf, Baptiste (Auteur de la Conférence)
CIRM (Editeur )
05C10 - Planar graphs; geometric and topological aspects of graph theory
CIRM (Editeur )
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Résumé :
In this talk, we consider two models of random geometry of surfaces in high genus: combinatorial maps and hyperbolic surfaces. The geometric properties of random hyperbolic surfaces under the Weil–Petersson measure as the genus tends to infinity have been studied for around 15 years now, building notably on enumerative results of Mirzakhani. On the other hand, random combinatorial maps were first studied in the planar/finite genus case, and then in the high genus regime starting 10 years ago with unicellular (i.e. one-faced) maps. In a joint work with Svante Janson, we noticed some numerical coincidence regarding the counting of short closed curves in unicellular maps/hyperbolic surfaces in high genus (comparing it to results of Mirzakhani and Petri). This leads us to conjecture some similarities between the two models in the limit, and raises several other open questions.
Keywords : hyperbolic surfaces
Codes MSC : Keywords : hyperbolic surfaces
05C10 - Planar graphs; geometric and topological aspects of graph theory
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 23/10/2023 Date de captation : 05/10/2023 Sous collection : Research talks arXiv category : Probability ; Combinatorics ; Geometric Topology Domaine : Geometry ; Topology Format : MP4 (.mp4) - HD Durée : 00:48:23 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-10-05_louf.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Probability and Geometry in, on and of non-Euclidian spaces / Probabilités et géométrie dans, sur et des espaces non-euclidiensOrganisateurs de la rencontre : Curien, Nicolas ; Garcia-Failde, Elba ; Petri, Bram ; Singh, Arvind Dates : 02/10/2023 - 06/10/2023 Année de la rencontre : 2023 URL Congrès : https://conferences.cirm-math.fr/2897.html
Données de citation
DOI : 10.24350/CIRM.V.20099303Citer cette vidéo: Louf, Baptiste (2023). Combinatorial maps and hyperbolic surfaces in high genus. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20099303 URI : http://dx.doi.org/10.24350/CIRM.V.20099303 |
Voir aussi
- [Multi angle] On the length spectrum of random hyperbolic 3-manifolds / Auteur de la Conférence Roig Sanchis, Anna.
- [Multi angle] Crossing the line: from graphs to curves / Auteur de la Conférence Parlier, Hugo.
- [Multi angle] Hyperbolic Voronoi percolation / Auteur de la Conférence Müller, Tobias.
- [Multi angle] Tail bounds for detection times in mobile hyperbolic graphs / Auteur de la Conférence Mitsche, Dieter.
- [Multi angle] Irreducibility of random polynomials / Auteur de la Conférence Kozma, Gady.
- [Multi angle] Non-perturbative topological recursion and Weil-Petersson volumes / Auteur de la Conférence Gregori, Paolo.
- [Multi angle] Geometry of large genus flat surfaces / Auteur de la Conférence Goujard, Élise.
- [Multi angle] Resurgent large genus asymptotics of intersection numbers / Auteur de la Conférence Giacchetto, Alessandro.
- [Multi angle] Integration on Grassmannians and deformed monotone Hurwitz numbers / Auteur de la Conférence Do, Norman.
- [Multi angle] Parking on the infinite binary tree / Auteur de la Conférence Contat, Alice.
- [Multi angle] Distances and isoperimetric inequalities in random maps of large genus / Auteur de la Conférence Chapuy, Guillaume.
- [Multi angle] Branching random walks and Martin boundaries: some properties, examples and counterexamples / Auteur de la Conférence Candellero, Elisabetta.
- [Multi angle] The geometry of random genus-0 hyperbolic surfaces via trees / Auteur de la Conférence Budd, Timothy.
Bibliographie
- JANSON, Svante et LOUF, Baptiste. Unicellular maps vs. hyperbolic surfaces in large genus: Simple closed curves. The Annals of Probability, 2023, vol. 51, no 3, p. 899-929. - http://dx.doi.org/10.1214/22-AOP1601
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