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.
Mots-Clés : hyperbolic surfaces
Codes MSC : Mots-Clés : 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 Catégorie arXiv : Probability ; Combinatorics ; Geometric Topology Domaine(s) : Géométrie ; Topologie Format : MP4 (.mp4) - HD Durée : 00:48:23 Audience : Chercheurs ; Etudiants Science Cycle 2 ; 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 de la Rencontre : 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 |
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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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