Professor: Leonid Koralov, Department of Mathematics, University of Maryland 
Title: Large Time Behavior of Randomly Perturbed Dynamical Systems 
Abstract: We will discuss several asymptotic problems for randomly perturbed flows
(and related problems for Markov chains with rare transitions). One class of flows (with regions where a strong flow creates a trapping mechanism) leads to a new class of elliptic and parabolic boundary value problems with
nonstandard boundary conditions. The same boundary value problems appear as a limiting object when studying the
asymptotic behavior of diffusion processes with pockets of large diffusivity.
We will also discuss how largedeviation techniques can be used
to study the asymptotic behavior of solutions to quasilinear parabolic equations with a small parameter at the
second order term and the long time behavior of the corresponding diffusion processes.
