Analysis Seminar

Title: An example of hypoellipticity in infinite dimensions
Speaker: Tai Melcher
Speaker Info: University of Virginia
Brief Description:
Special Note: This is a specially arranged seminar to accommodate the visitor's schedule.

A collection of vector fields on a manifold satisfies H\"{o}rmander's condition if any two points are connected by a path whose tangent vectors only lie in the given directions. It is well-known that a diffusion which is allowed to travel only in these directions is smooth, in the sense that its transition probability measure is absolutely continuous with respect to the volume measure and has a strictly positive smooth density.

Smoothness results of this kind in infinite dimensions are typically not known, the first obstruction being the lack of an infinite-dimensional volume measure. We will discuss recent results on a particular class of infinite-dimensional spaces, where we have shown that vector fields satisfying H\"{o}rmander's condition generate a diffusion which has a strictly positive smooth density with respect to an appropriate reference measure.

Date: Thursday, May 1, 2014
Time: 4:10pm
Where: Lunt 105
Contact Person: Prof. Jared Wunsch
Contact email: jwunsch@math.northwestern.edu
Contact Phone: 847-491-5580
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