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Riemannian geometry and heat kernel analysis on some infinite-dimensional Lie groups

Masha Gordina

Abstract

We will talk about how curvature of an infinite-dimensional curved space effects the behaviour of Gaussian type measures. In particular, several settings for infinite-dimensional Lie groups will be considered: Hilbert-Schmidt groups which are natural infinite-dimensional analogues of matrix groups, Heisenberg infinite-dimensional groups modelled over an abstract Wiener space, and the homogeneous space Diff(S^1)/S^1 associated with the Virasoro algebra. We will describe what is known about the Ricci curvature in each of the case, and how its boundness (or unboundness) is reflected in the heat kernel (Gaussian) measure behaviour. The work on the Heisenberg group is joint with Bruce Driver.

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