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Abstract Wiener groups

Connections for Women: geometry and probability in high dimensions August 17, 2017 - August 18, 2017

August 18, 2017 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Tai Melcher (University of Virginia)
Location: MSRI:
Tags/Keywords
  • heat kernel measure

  • hypoellipticity

  • infinite-dimensional Lie group

  • quasi-invariance

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

6-Melcher

Abstract

Gaussian measure has for decades been recognized as the appropriate measure to use in infinite-dimensional analysis, and calculus on such measure spaces has become a valuable tool in the analysis of stochastic processes and their applications. For infinite-dimensional curved spaces, the analogue of Gaussian measure is heat kernel measure. 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 hypoelliptic structure, and we're able to show smoothness results for heat kernel measures under both elliptic and hypoelliptic conditions. Parts of this talk are based on joint work with F. Baudoin, D. Dobbs, B. Driver, N. Eldredge, and M. Gordina.

Supplements
29337?type=thumb Melcher Notes 297 KB application/pdf Download
Video/Audio Files

6-Melcher

H.264 Video 6-Melcher.mp4 112 MB video/mp4 rtsp://videos.msri.org/data/000/029/222/original/6-Melcher.mp4 Download
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