Combinatorial maps and hyperbolic surfaces in high genus | Vidéo | Carmin.tv

00:00:00 / 00:00:00

Combinatorial maps and hyperbolic surfaces in high genus

De Baptiste Louf

hyperbolic surfaces

Apparaît dans la collection : Probability and Geometry in, on and of non-Euclidian spaces / Probabilités et géométrie dans, sur et des espaces non-euclidiens

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.

Informations sur la vidéo

Date de captation 05/10/2023
Date de publication 23/10/2023
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20099303
Citer cette vidéo Louf, Baptiste (05/10/2023). Combinatorial maps and hyperbolic surfaces in high genus. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20099303
URL https://dx.doi.org/10.24350/CIRM.V.20099303

Domaine(s)

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

Codes MSC

05C10 Planar graphs; geometric and topological aspects of graph theory

Dernières questions liées sur MathOverflow

Pour poser une question, votre compte Carmin.tv doit être connecté à mathoverflow

Poser une question sur MathOverflow

Copyright Carmin.tv 2024

Donner son avis