Isaac Chavel and Edgar Feldman will continue their investigations of the effect of small perturbations of a manifold on the spectral and stochastic properties of the manifold. These investigations have progressed from studying the relation of eigenvalues of the Laplacian to the geometry and topology of the manifold to consideration of probabilistic formulations of these questions. The particular perturbations of the manifolds to be studied include adding long thin handles, deleting tubular neighborhoods of submanifolds or removing small domains. The investigators will also consider large time asymptotics of Brownian motion and heat diffusion.
