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Combinatorial maps and hyperbolic surfaces in high genus
Multi angle
Authors : ... (Author of the conference)
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05C10 - Planar graphs; geometric and topological aspects of graph theory
... (Publisher )
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Abstract :
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
MSC Codes : Keywords : hyperbolic surfaces
05C10 - Planar graphs; geometric and topological aspects of graph theory
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Information on the Video
Language : EnglishAvailable date : 23/10/2023 Conference Date : 05/10/2023 Subseries : Research talks arXiv category : Probability ; Combinatorics ; Geometric Topology Mathematical Area(s) : Geometry ; Topology Format : MP4 (.mp4) - HD Video Time : 00:48:23 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-10-05_louf.mp4 
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Information on the Event
Event Title : Probability and Geometry in, on and of non-Euclidian spaces / Probabilités et géométrie dans, sur et des espaces non-euclidiensDates : 02/10/2023 - 06/10/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2897.html
Citation Data
DOI : 10.24350/CIRM.V.20099303Cite this video as: (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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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
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