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Jérémie Bettinelli
École polytechnique
Laboratoire d'informatique (LIX)
91128 Palaiseau Cedex
FRANCE
Email: firstname « . » lastname « at » normalesup « . » org
Office: 2023
Phone: (+33) (0)1 77 57 80 61



We continue to consider more general surfaces. Instead of the sphere with or without holes, we now look at surfaces of positive genus, that is, connected sums of tori. In plain English, the surface of genus 1 is a bike tube. To obtain the surface of genus 2, patch together 2 bike tubes as follows: cut a small disk out of each tube and glue the boundaries of these two disks together. Then, you may add to this another tube to get the surface of genus 3 and so on.
These are the objects we studied in The Topology of Scaling Limits of Positive Genus Random Quadrangulations, the main result being that, after a proper scaling, a uniform quadrangulation of a surface of fixed genus converges, in some sense, to a random metric space homeomorphic to the same surface.