# Gregory Lawler

Wolf Prize Laureate in Mathematics 2019

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.

Wolf Prize Laureate in Mathematics 2019