4thThomas Wolff
Memorial Lectures
in Mathematics

April 20, 22, and 25, 2005
4:15 p.m.
Room 151 Sloan


 

Speaker:

WENDELIN WERNER
Professor of Mathematics
University of Paris - Sud


Two-dimensional continuous random systems

Probability theory and statistical mechanics often focus on the behavior of a functional of a large random system, with microscopic random inputs that sometimes interact with each other. In many cases, the output is close to being deterministic when the system is very large. In “critical cases,” the outcome can however be random at any scale. The microscopic randomness then gives rise to a macroscopic continuous randomness and it is natural to try to understand it mathematically. This turns out to be rather difficult in general, but in some cases, it is possible thanks to an additional mathematical structure, and relates these random structures to other parts of mathematics.

An example is given by the scaling limit of critical two-dimensional particle systems, where particles interact locally. The understanding of these phenomena is related to complex analysis and to representation theory, as predicted by theoretical physicists. Mathematical progress has been made towards a better rigorous understanding of these models during the last years. I shall try to describe some of these recent ideas.

Most of the content of the lectures will be based on joint work with Greg Lawler and Oded Schramm.

 

werner.jpg (1881 bytes)  WENDELIN WERNER received his undergraduate degree from the École Normale Supériere in 1991.  Under the supervision of J.-F. Le Gall, he received his Ph.D. at the University Paris 6 in 1993 and his Habilitation in 1995. He is currently a professor at the Université Paris-Sud (Orsay) and a junior member of the Institute Universitaire de France.

 Dr. Werner was the winner of the Rollo Davidson Prize in 1998.  The following year, he was recognized with the Cours Peccot at Collège de France and the Paul Doistau-Emile Blutet Prize from the French Academy of Sciences.  He is also the winner of the European Mathematical Society Prize, the Fermat Prize, and the Jacques Herbrand Prize.

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The Thomas Wolff Memorial Lectures
In Mathematics

The Thomas Wolff lectures, sponsored by donations from his widow and his parents, memorialize Caltech’s great analyst who was tragically killed at age 46 in an automobile accident in July 2000.  Wolff was a specialist in analysis, particularly harmonic analysis. Professor Wolff made numerous highly original contributions to the mathematical fields of Fourier analysis, partial differential equations, and complex analysis. A recurrent theme of his work was the application of finite combinatorial ideas to infinite, continuous problems. 

His early work on the Corona theorem, done as a Berkeley graduate student, stunned the mathematical community with its simplicity.  Tom never wrote it up himself since several book writers asked for permission to include the proof in their books where it appeared not long after he discovered it.  After producing a number of very significant papers between 1980 and 1995, he turned to the Kakeya problem and its significance in harmonic analysis, works whose impact is still being explored. 

Peter Jones, professor of mathematics at Yale, described Tom’s contributions as follows:  “The hallmark of his approach to research was to select a problem where the present tools of harmonic analysis were wholly inadequate for the task. After a period of extreme concentration, he would come up with a new technique, usually of astonishing originality. With this new technique and his well-known ability to handle great technical complications, the problem would be solved. After a few more problems in the area were resolved, the field would be changed forever. Tom would move on to an entirely new domain of research, and the rest of the analysis community would spend years trying to catch up. In the mathematical community, the common and rapid response to these breakthroughs was that they were seen not just as watershed events, but as lightning strikes that permanently altered the landscape.”

Tom was noted for his analytic prowess, the depth of his insights, and the passion with which he nurtured the talents of young mathematicians.  We miss him.

 


For information and registration, please contact
Elizabeth Wood at (626) 395-4334 or
ewood@caltech.edu.
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