Parabolic PDE's and deterministic games
Robert V. Kohn (Courant Institute, NYU)

We usually think of parabolic partial differential equations and first-order Hamilton-Jacobi equations as being quite different. Parabolic equations are linked to random walks, and often arise as steepest-descents; Hamilton-Jacobi equations have characteristics, and often arise from optimal control problems. In truth, these equations are not so different. I will discuss recent work with Sylvia Serfaty, which provides deterministic optimal-control interpretations of many parabolic PDE. In some cases -- for example motion by curvature -- the optimal control viewpoint is very natural, geometric, and easy to understand. In other cases -- for example the linear heat equation -- it seems a bit less natural, and therefore even more surprising.

Colloquium, Department of Mathematics, Rice University
October 18, 2007