2011-2012 Milliman Lectures
Department of Mathematics
University of Washington

Wendelin Werner
Professor of Mathematics
Université Paris-Sud

Aspects of Conformal Invariant Randomness
During the last fifteen years, the mathematical understanding of random two-dimensional structures exhibiting conformally invariant features has made substantial progress - with several key contributions that have been taking place (and still are taking place!) in the Seattle area. The goal of these lectures will be to present some of the main underlying ideas in a self-contained way, accessible to non-specialists.

Lecture I: The Global Picture
4:00pm Tuesday, May 22nd - Savery Hall Room 260

Abstract: In this lecture, I will try to give an overview of some of the main ideas and results in the general area of two-dimensional random models - including the discussion of conformal invariance of discrete models, Schramm's SLE processes and their generalizations, planar maps, and some open questions.

Lecture II: Introduction to the Gaussian Free Field
4:00pm Wednesday, May 23rd - Smith Hall Room 205
(Note different room from Tuesday/Thursday)

Abstract: In this lecture, I will give an introduction to the Gaussian Free Field, its properties and how it can be related to SLE processes, and Conformal Loop Ensembles.

Lecture III: Conformal Loop Ensembles
4:00pm Thursday, May 24th - Savery Hall Room 260

Abstract: In this third lecture, I will focus more on some properties of the Conformal Loop Ensembles, including their precise relation to SLE and Brownian loops.

Bio: Wendelin Werner studied at the Ecole Normale Superieure 1987-91, and received his doctorate from the Universite Pierre-et-Marie-Curie in 1993 under the direction of Jean-Francois Le Gall. Werner's work straddles the dividing line between physics and mathematics, introducing new ideas and concepts combining probability theory and complex analysis to understand the critical phenomena in phase transitions, such as from liquid to gas. His work on stochastic Loewner evolution and the geometry of two-dimensional Brownian motion (with Gregory Lawler and Oded Schramm) helped to confirm the predictions of physicists based on conformal field theory.

As a tribute to the importance of his work, Wendelin Werner has received the Fermat Prize, the George Polya Prize, and in 2006, the Fields Medal.

He is a professor at the University of Paris-Sud, and a member of the French Academy of Sciences.