Thesis defense: Donnelly Phillips

Event date: Saturday, April 15, 2023

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Donnelly Phillips will defend the Ph.D. thesis on Monday, April 15. The title is

The Hypoelliptic Heat Kernel on Infinite-Dimensional Lie Groups: Heisenberg-Like Quasi-Invariance and the Taylor Isomorphism”.

The defense will be held at Kerchof 128 at 12:00 pm.

Everyone is invited to attend.

Abstract: The real-valued Gaussian distribution has a natural extension to infinite-dimensional vector spaces (via abstract Wiener space) and to finite-dimensional Lie groups (as the heat kernel measure). We may combine these 2 ideas to define the heat kernel measure on an infinite-dimensional (simply-connected graded nilpotent) Lie group G. This research considers two complications on these objects. Firstly, we restrict our attention to the hypoelliptic setting, in which the diffusion is only infinitesimally generated by a subset of the possible directions, called “horizontal’’ directions. Secondly, we allow for the possibility that there are infinitely-many “vertical’’ directions. Imposing both of these restrictions complicates the analysis, and will require specifying a generalization of the Hörmander (bracket-generating) condition. During this presentation, while we will touch on a quasi-invariance result, we will spend most of our time discussing the Taylor isomorphism, which classifies the space of “L2-holomorphic” functions on G.

Last updated: Tuesday, April 9, 2024