Mathematical Sciences: Stochastic Analysis and Geometry

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Research will continue on parallel programs in stochastic geometry and stochastic Lyapunov stability theory. In the former direction research will involve the recurrence of isotropic transport processes and a project on eigenfunction expansions, both in the context of Riemannian manifolds. The work on Lyapunov stability will investigate nonlinear oscillations and wave equations with boundary conditions. Continued support is also being provided for the Midwest Probability Colloquium, which now functions as a major annual event in the field of probability theory. Mathematical research in probability theory is used as a tool for modeling in both the physical and social sciences. This award will continue the development of these tools. In addition it will provide support for a meeting which has been very successful in bringing together research workers from many specialty areas.