Random Fractals Coming from 2-D Statistical Physics

Abstract

Mathematical models of phase transitions in 2-D statistical physics lead to random fractals. The speaker will introduce some of the discrete models (self-avoiding walk, loop-erased walk) and then describe the conformally invariant continuum limit, the Schramm-Loewner evolution (SLE). This is an example of a random fractal for which one can prove nontrivial facts about fractal and multifractal behavior. The speaker will discuss these including some recent results with various co-authors.

About the speaker

Prof. Gregory Lawler received his PhD from Princeton in 1979. He was on the faculty of Duke University from 1979 to 2001, and of Cornell University from 2001 to 2006. He joined the University of Chicago since 2006, where he is currently Professor of Mathematics and of Statistics.

Prof. Lawler has made very substantial and important contributions to random walk and also made groundbreaking contributions to the Schramm-Loewner evolution since 2000. He received the 2006 SIAM George Polya Price with Oded Schramm and Wendelin Werner. He is a Fellow of the American Academy of Arts & Sciences and the Institute of Mathematical Statistics. He was also a former editor of Annals of Probability. Currently, he is an editor of Journal of American Mathematical Society.