# Jean Francois le Gall

Wolf Prize Laureate in Mathematics 2019

**Jean Francois le Gall**

#### Affiliation at the time of the award:

**Université Paris-Sud ,France**

#### Award citation:

**“for his deep and elegant work on stochastic processes”.**

#### Prize Share:

**Jean Francois le Gall**

**Gregory Lawler**

Jean-François Le Gall (born in 1959, France) is a French mathematician working in areas of probability theory such as Brownian motion, Lévy processes, superprocesses and their connections with partial differential equations, the Brownian snake, random trees, branching processes, stochastic coalescence and random planar maps. He received his Ph.D. in 1982 under the supervision of Marc Yor. He is currently professor at the University of Paris-Sud in Orsay and is a senior member of the Institut universitaire de France.

Le Gall’s generation has a great impact on Probability or demonstrated more power and beauty in their arguments. He has been at the forefront of Probability since 1983, when he established what still are the best results on pathwise uniqueness for one-dimensional stochastic differential equations. His current groundbreaking discoveries on the Brownian map ensure he remains at the cutting edge of the field today. He has received the 1986 Rollo Davidson Prize the 2005 Grand Prix Sophie Germain, French Academy of Science, the 2005 Fermat prize in mathematics and was elected to French academy of sciences, December 2013.

Jean-François Le Gall has made several deep and elegant contributions to the theory of stochastic processes. His work on the fine properties of Brownian motions solved many difficult problems, such as the characterization of sets visited multiple times and the behavior of the volume of its neighborhood – the Brownian sausage. Le Gall made groundbreaking advances in the theory of branching processes, which arise in many applications. In particular, his introduction of the Brownian snake and his studies of its properties revolutionized the theory of super-processes – generalizations of Markov processes to an evolving cloud of dying and splitting particles. He then used some of these tools for achieving a spectacular breakthrough in the mathematical understanding of 2D quantum gravity. Le Gall established the convergence of uniform planar maps to a canonical random metric object, the Brownian map, and showed that it almost surely has Hausdorff dimension 4 and is homeomorphic to the 2-spher.