Probability and Combinatorics Seminar

  • Date: –18:15
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 4006
  • Lecturer: Baptiste Louf
  • Organiser: Matematiska institutionen
  • Contact person: Clément Requilé
  • Seminarium

The geometry of high genus maps

Abstract:

A map is the result of polygons glued together to form a (compact, connected, oriented) surface. Alternatively, one can think of it as a graph embedded in a surface. Just like graphs, maps are a good model of discrete geometry, and it can be interesting to study their properties, especially when considering random maps whose size goes to infinity.

In this talk I will present some results about high genus maps. The genus of a map is the number of handles of the surface it lives on (for instance, a sphere has genus 0 and a torus has genus 1), and high genus maps are defined as (sequences of) uniform random maps whose size and genus go to infinity at the same time.

There won’t be any proof or other technical details, but I will present a bunch of open problems and conjectures.