3rd Thomas Wolff
Memorial Lectures
in Mathematics

April 26, 27 and May 4, 5, 2004
4:15 p.m.
Room 151 Sloan


 

Speaker:

JEAN BOURGAIN
Professor of Mathematics
Institute for Advanced Study
Princeton, NJ
J.L. Doob Professor of Mathematics
University of Illinois
Urbana, IL


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 continuation.

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.
 


bourgain.jpg (1881 bytes)  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.

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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, mathematics department chair 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
Liz Wood at (626) 395-4334 or
ewood@caltech.edu.
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