Steven Flynn

Steven Flynn
University of Bath | UB · Department of Mathematical Sciences

Doctor of Philosophy
Research Project Grant funded by the Leverhulme Trust. RPG-2020-037: Quantum limits for sub-elliptic operators.

About

3
Publications
63
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Additional affiliations
September 2014 - June 2020
University of California Santa Cruz
Position
  • PhD Student
Education
September 2014 - June 2020
University of California, Santa Cruz
Field of study
  • Mathematics

Publications

Publications (3)
Preprint
Full-text available
In this paper, we consider the semi-classical setting constructed on nilpotent graded Lie groups by means of representation theory. We analyze the effects of the pull-back by diffeomorphisms on pseudodifferential operators. We restrict to diffeomorphisms that preserve the filtration and prove that they are Pansu differentiable. We show that the pul...
Article
Full-text available
We initiate the study of X-ray tomography on sub-Riemannian manifolds, for which the Heisenberg group exhibits the simplest nontrivial example. With the language of the group Fourier transform, we prove an operator-valued incarnation of the Fourier Slice Theorem, and apply this new tool to show that a sufficiently regular function on the Heisenberg...
Preprint
Full-text available
We initiate the study of X-ray tomography on sub-Riemannian manifolds, for which the Heisenberg group exhibits the simplest nontrivial example. With the language of the group Fourier Transform, we prove a operator-valued incarnation of the Fourier Slice Theorem, and apply this new tool to show that a sufficiently regular function on the Heisenberg...

Projects

Project (1)
Project
Develop a robust noncommucative semi-classical symbol calculus for pseudodifferential operators on sub-Riemannian manifolds by means of representation theory. Characterize semi-classical measures for sublaplacians and prove quantum ergodicity in new cases. Funded by Leverhulme Trust Grant (RPG-2020-037: Quantum limits for sub-elliptic operators) with Veronique Fischer (PI) and Clotilde Fermanian Kammerer (Co-PI).