EVENT DETAILS AND ABSTRACT

Title: Analysis and Geometry of the Path space over a Riemannian Manifold
Speaker: Elton Hsu
Speaker Info: Northwestern
Brief Description:
Special Note:
Abstract:

The path space over a Riemannian manifold is the space of continuous maps from the unit time interval to the manifold. It is a typical infinite dimensional manifolds. We will show how to introduce natural concepts of volume measure, gradient, and a Hilbert structure on its tangent spaces. Under this basic setting we can study analytic and geometric properties of the path space centered around the so-called Ornstein-Uhlenbeck operator, the counterpart of the Laplace-Beltrami operator in the current context. We will clarify the role stochastic analysis plays in this study. We will give a survey of some old and new results and discuss several interesting open problems for further research. The talk should be accessible to the general audience with a good grasp of first year graduate level measure theory and functional analysis.