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Ravi Srinivasan : Kinetic theory for shock clustering and Burgers turbulence

A remarkable model of stochastic coalescence arises from considering shock statistics in scalar conservation laws with random initial data. While originally rooted in the study of Burgers turbulence, the model has deep connections to statistics, kinetic theory, random matrices, and completely integrable systems. The evolution takes the form of a Lax pair which, in addition to yielding interesting conserved quantities, admits some rather intriguing exact solutions. We will describe several distinct derivations for the evolution equation and, time-permitting, discuss properties of the corresponding kinetic system. This talk consists of joint work with Govind Menon (Brown).

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