The Wolf Prize for Mathematics is awarded to Gregory Lawler from Chicago University, for his comprehensive and pioneering research on erased loops and random walks and to Jean-François Le Gall from Paris Sud Orsay University, for his profound and elegant works on stochastic processes. The work undertaken by these two mathematicians on loops and probability, which have been recognized by multiple prizes, became the stepping stone for many consequent breakthroughs.

Jean-François Le Gall (Photo by F. Hullin)

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-sphere.

Gregory Lawler

Gregory Lawler has made trailblazing contributions to the development of probability theory. He obtained outstanding results regarding a number of properties of Brownian motion, such as cover times, intersection exponents and dimensions of various subsets. Studying random curves, Lawler introduced a now classical model, the Loop-Erased Random Walk (LERW), and established many of its properties. While simple to define, it turned out to be of a fundamental nature, and was shown to be related to uniform spanning trees and dimer tilings. This work formed much of the foundation for a great number of spectacular breakthroughs, which followed Oded Schramm’s introduction of the SLE curves. Lawler, Schramm and Werner calculated Brownian intersection exponents, proved Mandelbrot’s conjecture that the Brownian frontier has Hausdorff dimension 4/3 and established that the LERW has a conformally invariant scaling limit. These results, in turn, paved the way for further exciting progress by Lawler and others.

The awarding ceremony will be in May 2019 in Israel. Since 1978, five or six Wolf Prizes have been awarded annually in the Sciences; prize fields comprise agriculture, chemistry, mathematics, medicine and physics. The prize in each field consists of a certificate and a monetary award of $100,000, shared between recipients.