Title: Smoothness of heat kernel measures on abstract Wiener groups
Speaker: Tai Melcher (Associate Professor, University of Virginia)
Abstract: Smoothness is a fundamental principle in the study of measures on infinite-dimensional spaces. Smoothness properties on such measure spaces has allowed, for example, the development of a calculus which has become a valuable tool in the analysis of stochastic processes and their applications. Canonical examples of smooth measures include those induced by a Brownian motion, both its end point distribution and as a real-valued path. Heat kernel measure is the law of a Brownian motion on a curved space, and as such is a natural object for study of smoothness properties. We’ll discuss heat kernel measures in a special class of infinite-dimensional spaces and provide motivation for the construction. In particular, these spaces admit a natural geometry which is in some sense degenerate but still allows for smoothness properties of the measures.