Thomas Wolff Memorial Lectures
in Mathematics

November 27, 29; December 4, 6, 2001
4:15 p.m.  Room 151 Sloan




Chair, Department of Mathematics
Herbert E. Jones, Jr. Professor
of Mathematics
Princeton University


Tuesday, November 27, 2001
Sharp fronts for incompressible fluids

A simple condition rules out the
formation of certain types of singularities
in 2-dimensional fluids


Thursday, November 29, 2001
Local conformal invariants

An explanation of a procedure to
construct local invariants from a
conformal metric, including "Q curvature"
and "renormalized volume"


Tuesday, December 4, 2001
Domination of
pseudodifferential operators

A discussion of two given
pseudodifferential operators A and B
having the property that Af has larger
2 norm than Bf  for any function f


Thursday, December 6, 2001
Hedging of options with
transaction costs

Black and Scholes showed how to
hedge an option perfectly if one can trace
without transaction costs. This talk discusses
how well one can hedge in the presence
of transaction costs.



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CHARLES FEFFERMAN is one of the major analysts of the 20th century. He was a prodigy who delved into his father’s calculus books at age 10, and started classes at Maryland as a 12-year-old, graduating with high honors in math and physics at 17. Three years later, he added a Princeton doctorate to his credentials. Then began a series of “youngest ever’s” including a full professorship (at University of Chicago) at age 22, the youngest to hold that rank at the time; the youngest recipient of the prestigious Fields Medal; awarded every four years to a mathematician under 40 and considered mathematics’ equivalent of the Nobel; the first winner of the Waterman Prize; and the youngest person elected to the US National Academy of Sciences since the early 19th century.

In 1974, Fefferman joined the faculty at Princeton where he remains today as the Herbert E. Jones Jr. Professor of Mathematics and Mathematics Department Chair.

Of course, what matters to mathematicians is the string of deep insights and theorems that Charlie has produced, not the honors he has garnered. His work has impacted classical harmonic analysis, complex manifold theory, partial differential equations, and even mathematical physics and mathematical economics. His discovery of BMO duality theory for H1 spaces made previously subtle and complex results into simple corollaries. His work on singular integrals provided a new proof of Carleson’s result on the almost everywhere convergence of L2-fourier series. His work on canonical transformations and uncertainty principle bounds provided important new tools in PDEs. His discovery and masterful analysis of the logarithmic singularity of the Bergmann metric proved regularity of biholomorphic maps up to the boundary. His work with Seco on the binding energy of large Z atoms went far beyond the earlier results of Lieb-Simon and of Hughes-Siedentop-Weikard.

The breadth of Fefferman’s interest and scope can be seen in the series of Wolff lectures he’ll be giving on four different areas of analysis.


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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.


Wolff Banquet
For information, please contact Elizabeth Wood
at (626) 395-4334 or
Math Department Home Page