January 27th, 2021
Lecture: 12:00 - 12:55 p.m. (Pacific Standard Time)
Dr. Jean-Francois Le Gall
Professor of Mathematics, Université Paris-Saclay
Brownian Geometry on the Sphere
Much recent work has been devoted to the metric properties of large random graphs drawn on the two-dimensional sphere, which are also called random planar maps. Starting from a triangulation of the sphere with a given number of faces (triangles) and chosen uniformly at random, one considers the metric space consisting of the vertex set of this triangulation equipped with the graph distance.When the size of the triangulation tends to infinity, this suitably rescaled random metric space converges in distribution, in the Gromov-Hausdorff sense, to a random compact metric space called the Brownian sphere (or Brownian map). We will survey recent results showing that the Brownian sphere is, indeed, a universal model of random geometry in two dimensions. If time permits, we will also introduce related models such as the Brownian disk and the Brownian plane, and we will discuss their connections with the Brownian sphere.
The speaker will be available for an informal questions and answers session and discussion for half-an-hour following the lecture.
Bio: Professor Jean-Francois Le Gall is a distinguished French mathematician working in probability theory (including the theory of Brownian motion), random trees, the Brownian snake, stochastic processes and their connections with partial differential equations.He is a member of the French Academy of Sciences and was awarded the Davidson Prize (in 1986), the Fermat Prize (in 2005), as well as (in 2019) the Wolf Prize in Mathematics. He was awarded his Ph.D. in 1982 from the Université Pierre et Marie Curie (Paris VI) and is a Professor at the Université Paris-Sud Orsay, now part of the Université Paris-Saclay.
Wednesday, January 27 at 12:00pm to 12:55pm
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