Probability Seminar Department of Statistics and Department of Mathematics Wednesday, October 16, 2002 3:30 PM in REC 317 Professor Pat McDonald New College, Florida will speak on Brownian Motion, Dirichlet Spectrum and Heat Content Abstract Using exit time moments of Brownian motion, we construct invariants for smoothly bounded domains in complete Riemannian manifolds. We examine the connection between our invariants and the geometry of the underlying domain (both spectral and differential). We examine the connection between our invariants and isoperimetric conditions for the ambient manifold. Finally, we describe results which indicate that our invariants distinguish the isospectral nonisometric pairs of planar polygonal domains constructed by Buser, Conway, Doyle and Semmler.

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