(joint work with Svante Janson)

Combinatorial maps are discrete surfaces built by gluing polygons along their sides. They have many deep connections to combinatorics, computer science, algebra or statistical physics, but in this talk we are going to consider them from a probabilistic viewpoint, by studying the geometry of large random maps in the regime where both the size and the genus go to infinity.

In this work, we consider a particular model of maps (« unicellular maps »), and we study the law of simple closed curves on our maps. Surprisingly, we obtain the exact same limit law as Mirzakhani and Petri who studied the same problem on random hyperbolic surfaces in large genus under the Weil-Petersson measure. This leads us to conjecture that these two models are somehow "the same" in the limit.

https://umich.zoom.us/j/97288641488 Speaker(s): Baptiste Louf (Uppsala University)