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8th Annual Thomas Wolff Memorial Lecture
in Mathematics
January 13, 14, 20 and 21

4:15 p.m.  151 Sloan

Andrei Okounkov
Professor of Mathematics
Princeton University

The algebra and geometry of random surfaces

There exist deep and perhaps surprising connections between certain random surface models of direct probabilistic interest and algebraic geometry.  The random surface models in question are rather simple: these are the so-called stepped surfaces, also known as 3D Ising interfaces at zero temperature, and their close relatives. Various matrix models may be also viewed as more distant members of the same family.  The connections between these models and algebraic geometry go both ways. On the one hand,  enumerative problems related to algebraic curves may be answered in terms of partition functions of random surface models with specific boundary conditions. On the other hand, the analysis of random surfaces models, including such basic questions as the law of large numbers and the fluctuations around it is controlled by some different geometry, which is, in a sense, the "probabilistic mirror" to the original enumerative problem. I'll try to explain both directions of this correspondence in my lectures."

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Andrei Okounkov received his doctorate at Moscow State University in 1995 under Alexander Kirillov and Grigori Olshanski. He worked at the University of Chicago and the University of California at Berkeley before joining the faculty of Princeton University in 2002.

Okounkov's interests include representation theory, algebraic geometry, combinatorics, and mathematical physics. His results in asymptotic combinatorics include the first proof of the Baik-Deift-Johansson conjecture, which states that the asymptotics of random partitions distributed according to the Plancherel measure coincides with that of the eigenvalues of large Hermitian matrices. The new techniques that he developed for working with random partitions have found applications in ergodic theory, the study of random surfaces, and algebraic geometry.

Okounkov won the European Mathematical Society Prize in 2004 and the Fields Medal in 2006.

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You are invited to attend a dinner following the Thomas Wolff Memorial Lectures in Mathematics at The Athenaeum on Tuesday, January 13, 2009

Host bar   5:45 p.m.
Dinner  6:30 p.m.
Main Lounge

Reservations Required


Baby Spinach Frisee
kalamata olives, red onion, feta cheese, tomato, cucumber and Greek dressing

Grilled Chicken Breast
wild mushroom risotto, sweet pea emulsion and broccolini

Chocolate Whiskey Cake
chocolate and raspberry sauces

Please indicate if you require a vegetarian or kosher meal

For reservations, please contact Stacey V. Croomes at 626-395-4336 or send payment by Thursday,
January 8, 2009 made out to Caltech for $35.00 per person to:

Stacey V. Croomes

Caltech 253-37

Pasadena, CA  91125

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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, 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.

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