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
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.
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.
The Thomas Wolff
Thomas Wolff lectures, sponsored by donations from his widow and his parents, memorialize
Caltechs 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.
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.
Jones, professor of mathematics at Yale, described Toms 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.
was noted for his analytic prowess, the depth of his insights, and the passion with which
he nurtured the talents of young mathematicians. We