Curriculum Vitae
Research Interests
Hypoelliptic PDEs. Microlocal Analysis. Geometric Inverse Problems. Sub-Riemannian Geometry.
Employment
2024 – present Postdoctoral Fellow, University College London
2023 – 2024 Postdoctoral Fellow, University of Padova
2021 – 2023 Postdoctoral Fellow, University of Bath
2014 – 2020 Graduate Student Instructor & Graduate Teaching Assistant, University of California, Santa Cruz
Education
2014 – 2020 Ph.D. Mathematics, University of California, Santa Cruz
Dissertation: "Unraveling Geodesic X-ray Transforms on the Heisenberg Group"
Co-advisors: François Monard, Richard Montgomery
Dissertation: "Unraveling Geodesic X-ray Transforms on the Heisenberg Group"
Co-advisors: François Monard, Richard Montgomery
2014 – 2015 M.A. Mathematics, UCSC
2012 – 2014 B.A. Mathematics, UCSC
Research Papers
- Davide Barilari and Steven Flynn. Refined Strichartz estimates for sub-Laplacians in Heisenberg and H-type groups. arXiv:2501.04415, 2025.
- Clotilde Fermanian-Kammerer, Véronique Fischer, and Steven Flynn. A microlocal calculus on filtered manifolds. arXiv:2412.17448, 2024. Recommended for acceptance in Memoirs of the European Mathematical Society.
- Steven Flynn. The sub-Riemannian X-ray Transform on H-type Groups; Fourier Slice Theorems and Injectivity Sets. arXiv:2312.00594, 2023.
- Clotilde Fermanian-Kammerer, Véronique Fischer, and Steven Flynn. Geometric invariance of the semi-classical calculus on nilpotent graded Lie groups. Journal of Geometric Analysis, 2023.
- Steven Flynn. Singular Value Decomposition of the X-ray Transform on the Reduced Heisenberg group, and a Two-Radius Theorem. Springer, Trends in Mathematics: Ghent Analysis and PDE Center, 2023.
- Clotilde Fermanian-Kammerer, Véronique Fischer, and Steven Flynn. Some Remarks on Semi-Classical Analysis on Two-Step Nilmanifolds. Springer INdAM Series, 2022.
- Steven Flynn. Injectivity of the Heisenberg X-ray transform. Journal of Functional Analysis, 280.5 (2021): 108886.
Selected Talks
Upcoming
Dec 2025 Geometric Structures Seminar, SISSA
Dec 2025 HADES Seminar, UC Berkeley
Strichartz Estimates on H-type Groups
May 2025 UC Santa Cruz
Jan 2025 Lund University
Dec 2024 University College London
A Microlocal Calculus on Filtered Manifolds
Jan 2025 University College London
May 2024 Dispersion and Geometry in Padova
The sub-Riemannian X-ray Transform on H-type Groups
Nov 2023 Junior Methusalem Seminar, Ghent University
Oct 2023 University College London
Nov 2022 Geometry and Analysis Seminar, University of Bristol
Remarks on the Semi-classical Analysis of Step 2 Nilpotent Groups
May 2023 Operator Algebras in the South of the UK, University of Southampton
Mar 2023 CAGE mini-seminar, Sorbonne Université
Geometric Invariance of the Semi-Classical Calculus on Graded Lie Groups
Nov 2022 Conference on Noncommutative Analysis and PDEs, Queen Mary University
The Heisenberg X-ray Transform
May 2022 Analysis and Differential Geometry International Seminar, University of Aveiro
Mar 2022 AGeNT Seminar, University of Bath
Nov 2021 Problèmes Spectraux en Physique Mathématique, Institut Henri Poincaré
Sep 2021 Bath Analysis Seminar, University of Bath
Apr 2021 Sub-Riemannian Seminars (online)
May 2020 UCSC Geometry and Analysis Seminar
Integral Geometry on Contact Manifolds
Jan 2020 Joint Math Meeting, Denver, Colorado
Nov 2019 Mathematical Sciences Research Institute, Berkeley, CA
Sep 2019 MSRI, Berkeley, CA
Service
2022 Organizer, Bath Analysis Seminar
2022 Organizer, University of Bath Postdoc Away Day
2019 Organizer, Graduate Student Seminar, MSRI
2018 Organizer, Microlocal Analysis Seminar, UCSC
2018 Organizer, Graduate Differential Geometry Seminar, UCSC
Professional Activities
2025 Participant, MPS Workshop on LEAN
2019 Program Associate, MSRI Microlocal Analysis Program
2018 Mentor, UCSC Directed Reading Program
Teaching
University College London
Fall 2025 Math 0071: Spectral Theory
University of California, Santa Cruz
Summer 2019 Math 105A: Real Analysis
Spring 2019 Math 105B: Real Analysis
Summer 2018 Math 105A: Real Analysis
Summer 2017 Math 3: Precalculus
Graduate Teaching Assistant
2014–2020: Calculus sequence (Math 11A, 19A/B, 23A/B), Linear Algebra (Math 21), Real Analysis (Math 105A/B), Introduction to Proofs (Math 100), Programming for Mathematics (Python, Math 152), Precalculus (Math 3), College Algebra (Math 2), and Introduction to Physics (Physics 5/5L).