00:00:00 / 00:00:00

Combinatorial maps and hyperbolic surfaces in high genus

By Baptiste Louf

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

Citation data

  • DOI 10.24350/CIRM.V.20099303
  • Cite this video Louf Baptiste (10/5/23). 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


  • 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

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow


  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
  • Get notification updates
    for your favorite subjects
Give feedback