Workshops for Probabilistic Methods in Mathematical Physics

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This is a proposal for partial funding of two workshops in the second year of the 2008-9 thematic year program of Probabilistic Methods in Mathematical Physics at the CRM (Centre de Recherches Mathematiques). The full program, now in progress, consists of 10 interrelated workshops on central topics in mathematical physics which are closely connected to probability theory. Six workshops are being funded by a grant from NSF/DMS. Two of the workshops. now complete, were funded a total of $10K by NSF grant PHY0757940. The current proposal asks for the same amount for the remaining two workshops. The requested funding is to pay the travel and hotel expenses of 10 younger US participants; graduate students, post-docs or junior faculty members at a U.S. university without an NSF grant. Intellectual Merit: Probablilistic methods have long been central in physics and mathematics, and their significance has only increased in recent years. The development of the Schramm-Loewner evolution and its applications by Lawler, Schramm, Smirnov, Werner and others in statistical mechanics is one important example. Another is the recent work of Okounkov, Nekrasov, Kenyon and others on the use of random partitions to determine partition functions of models in gauge theory. Yet another are applications of random fields by Bousso-Polchinski, Douglas and others to landscape statistics in string/M theory. The number and rate of developing topics is large. The time is ripe for a year long review of the probabalistic methods and their applications through a series of coordinated workshops and lecture series. Broader Impact: The program is by nature inter-discipinary, and the workshops are designed to bring together mathematicians and physicists from differing research traditions working on closely related problems . This cross-fertilization has already had an enormous impact on contemporary mathematics. Many contemporary physicists have in return been highly influenced by the mathematical developments. In addition to the impact on established researchers, the program will bring in many graduate students, post-docs and other young researchers, exposing a new generation of researchers to this fast developing area.