Introduction to the theory of random planar maps.
ABSTRACT: A (planar) map is a finite connected planar graph given with an embedding in the plane.
The goal is to understand the large scale properties of a planar graph (or map) chosen uniformly at random in a certain class (e.g. triangulations or quadrangulations with n faces...). In a breakthrough paper, Chassaing and Schaeffer showed that the typical diameter of a quadrangulation with n faces is of order n^1/4. Since then, a lot of work has been done culminating with the recent characterization of the so-called Brownian Map by Le Gall and Miermont. If the metric structure of large maps is by now (quite-)well-understood , a lot of challenging open questions remain open...
BIO:
Nicolas Curien recently completed his PhD with Jean Francois Le Gall.
Currently he works at the Ecole Normale Superiore in Paris, where he investigates the structure of random planar maps along with many other topics in probability theory.