# Aisenstadt Chairs 2008-2009

**Wendelin Werner**(Paris-Sud, Orsay)

August 1-12, 2008

Series of conferences

Wendelin Werner is a specialist of probability theory. He obtained his doctorate in 1993 under the supervision of Jean-François Le Gall. He has been Professor at the Laboratoire de mathématiques of the Université Paris-XI since 1997, in the Laboratoire de mathématiques of Orsay, and also Professor of Mathematics at the École normale supérieure since 2005.

With his collaborators G. Lawler and O. Schramm, he has shown that the probability of two non-intersecting planar random walks decreases as n^(-5/8) where n is the length of the two walks and has determined the Hausdorff dimension (= 4/3) of the external boundary of planar brownian motion. His work on the stochastic Loewner equation (SLE) and conformal loop ensembles is expected to have a profound impact on the physical description of critical phenomena in two dimensions.

Werner received the Prix de la Société européenne de Mathématiques in 2000, the Prix Fermat in 2001, the Loève Prize in 2005, and the Pòlya Prize the following year. In 2006, he became the first probabilist to receive the Fields Medal.

**Craig Tracy** (California at Davis)

August 26 -31, 2008 and March 2009

Craig A. Tracy completed his doctorate at SUNY, Stony Brook under Barrry McCoy and then held postdoctoral positions at the University of Rochester (1973-1975) and the C.N. Yang Institute for Theoretical Physics (1975-1978). He was Professor at Dartmouth College before joining the University of California at Davis in 1984. He is currently Distinguished Professor of Mathematics at UC Davis.

In his joint work with Wu, McCoy and Barouch a connection was first discovered between exactly solvable statistical models, like the Ising model, and classical integrable systems, in particular the Painlevé transcendants. In more recent years, in collaboraiton with Harold Widom, he has obtained many crucial results on the theory of Fredholm and Toeplitz determinants, and random matrix theory. They introduced a new class of distributions, now called the Tracy-Widom distributions, governing the eigenvalues at the edge of the spectrum in the large N limit. These turned out to be "universal" in the sense that they also underlie the statistics of the longest increasing subsequence problem, several tiling problems, and various growth models.

He shared the George Pólya Prize in 2002 with his long-time collaborator Harold Widom, as well as the AMS-SIAM Norbert Wiener Prize in 2007. He is a member of the American Academy of Arts and Sciences.

**Andrei Okounkov** (Princeton)

September 1-16, 2008

The Algebra and Geometry of Random Surfaces

Andrei Okounkov received his doctorate at Moscow State University in 1995 under Alexander Kirillov. He was professor at the University of California at Berkeley until 2002, and then moved to Princeton University.

Okounkov's interests include representation theory, algebraic geometry, combinatorics, and mathematical physics. He is known in particular for his important results in asymptotic combinatorics. He gave the first proof of the Baik-Deift-Johansson conjecture, which states that the asymptotics of random partitions distributed according to the Plancherel measure coincide 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 theory of random surfaces and algebraic geometry.

Okounkov received a Sloan Research Fellowship in 2000 and a Packard Felowship in 2001. He won the European Mathematical Society Prize in 2004 and the Fields Medal in 2006.