Professor of Mathematics
Institute for Advanced Study
J.L. Doob Professor of Mathematics
University of Illinois
New encounters in combinatorial number theory
(from the Kakeya problem to cryptography)
We describe the relation to so-called
‘sum-product’ problems, the context of finite fields and new estimates on
Gauss sums and exponential sums related to the Diffie-Hellman distributions.
On random Schrödinger operators
We discuss spectral issues for operators
–Δ + V, V a random potential, with
emphasis on problems for D > 1, the Anderson-Bernoulli model, and unique
Ginzburg-Landau minimizers and related harmonic analysis issues
This will be a survey of new results around the 3D Ginzburg-Landau problem.
In particular, regularity of minimizers, control of phases and new
Hodge-type decompositions will be discussed.
JEAN BOURGAIN graduated from the Free
University of Brussels, Belgium in 1977 with a Ph.D in Mathematics and in
1979 earned a Habilitation Degree from the same university. He is currently
a professor at the Institute for Advanced Study at Princeton and is the J.L.
Doob Professor of Mathematics at the University of Illinois at
Urbana-Champaign. The French Academy has awarded Bourgain two awards: in
1985, the Langevin Prize and in 1990, the E. Cartan Prize. In 1994, Bourgain
received the Fields Medal. His research includes work in the geometry of
Banach spaces, convexity in high dimensions, harmonic analysis, ergodic
theory, and nonlinear partial differential equations.
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, mathematics department chair 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