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10th Annual Thomas Wolff Memorial Lecture
"Invariant manifolds and dispersive Hamiltonian evolution equations"
Abstract: By means of certain dispersive PDEs (such as the nonlinear
Klein-Gordon equation) we will exhibit a new family of phenomena
related to the ground state stationary solutions. These ground states are exponentially
unstable, and one can construct stable, (un)stable, and center(-stable) manifolds
associated with them in the sense of hyperbolic dynamics.
Wilhelm Schlag received his undergraduate education at the University of Vienna and his graduate education at the University of California at Berkeley and the California Institute of Technology. He obtained his Ph.D. degree in mathematics under Thomas Wolff in 1996 at Caltech. He has held faculty positions at Princeton University, Caltech, and the University of Chicago, as well as visiting positions at the Institute for Advanced Study, Princeton and the Mathematical Sciences Research Institute at Berkeley. He is currently a Professor of Mathematics at the University of Chicago. He is the author of more than fifty scholarly papers and acts as editor of Geometric and Functional Analysis, the Bulletin of the Mathematical Society of France, and Analysis & PDE. He has been an invited speaker at numerous national and international meetings, including the International Congress of Mathematical Physics in 2004 at Lisbon, Portugal.
The 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.
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 Wolff 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.