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

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Combinatorial maps and hyperbolic surfaces in high genus

By Baptiste Louf

hyperbolic surfaces

Appears in 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.

Information about the video

Date of recording 05/10/2023
Date of publication 23/10/2023
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20099303
Cite this video 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

Domain(s)

Bibliography

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

MSC codes

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

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