# Gregory Lawler

Wolf Prize Laureate in Mathematics 2019

**Gregory Lawler**

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

**The University of Chicago, USA**

#### Award citation:

**“for his extensive and groundbreaking research on random paths and loops”.**

#### Prize Share:

**Gregory Lawler**

**Jean Francois le Gall**

Gregory Francis Lawler (born in 1955) is an American mathematician working in probability theory and best known for his work since 2000 on the Schramm–Loewner evolution. Gregory Lawler received his Ph.D. from Princeton University in 1979 under the supervision of Edward Nelson. He was on the faculty of Duke University from 1979 to 2001, of Cornell University from 2001 to 2006, and since 2006 is at the University of Chicago. Lawler received the 2006 SIAM George Pólya Prize, in 2012 he became a fellow of the American Mathematical Society and Member, National Academy of Sciences in 2013.

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.