Title: The contribution of Jean François Le Gall to Brownian Geometry
Speaker: Hubert Lacoin – IMPA
Abstract: J.F. Le Gall has been awarded the Wolff prize in 2019 "for his profound and elegant works on stochastic processes". In this talk we wish to introduce to a large audience to Le Gall's contribution to the subject of Random Geometry (his main object of focus in the last 15 years). Our starting point is the following question:
"Is there a good notion of random sphere ?"
or more precisely:
"Is there a natural way to choose at random a manifold among all those that are homeomorphic to the sphere?"
In order to give a more precise meaning to the question and to explain the elegant answer brought to the above question by Le Gall and Miermont, we will make a detour to the world of discrete random geometry and the notion Quadragulations of the Sphere, and explore the path that lead to the construction of the Brownian Sphere via Brownian Motion, Brownian Tree, and Brownian Snake.