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Seminar Abstracts

Ravi Srinivasan, University of Texas at Austin and Duke University

Kinetic theory and Lax equations for shock clustering and Burgers turbulence

Abstract: The study of shock statistics in Burgers equation arises as a problem of fundamental interest in mathematical physics, among other areas. In statistics, it appears in the context of limit theorems with `cube-root' asymptotics, culminating in a remarkable analysis of the parabolic hull of Brownian motion by Groeneboom (1989). More recent work in stochastic coalescence (by Bertoin, Duchon, and others) has provided another viewpoint on this problem, from which we show a Lax pair is naturally derived. This fact, in addition to the form of some exact solutions, suggests that the model is completely integrable. If time permits I will also touch upon some interesting connections with random matrices. This is joint work with Govind Menon (Brown).

TUESDAY, November 17, 2009
Time: 1:30 P.M.
Location: PPB 300