About me
I am currently a Hans Rademacher Instructor at the University of Pennsylvania. My research interests are in Harmonic Analysis and related topics. I completed my PhD under the supervision of Jim Wright at the University of Edinburgh in 2022, having previously completed an integrated Master’s degree at the University of Warwick in 2018.
Research
I am interested in Harmonic Analysis, and in particular, uniform oscillatory integral estimates and their relation to uniform sublevel set estimates in the presence of additional qualitative, geometric structural assumptions. I am also interested in Geometric Measure Theory, and have recently been thinking about using methods of Harmonic Analysis and Incidence Geometry to solve problems in Geometric Measure Theory.
Publications and preprints:
1. “Lower bounds on L^p quasi-norms and the Uniform Sublevel Set Problem”, Mathematika 67 (2021) 296–323. Published version (open access): https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12076 Preprint: https://arxiv.org/abs/2008.01708
2. “Oscillating spectral multipliers on groups of Heisenberg type”, Rev. Mat. Iberoam., joint work with Roberto Bramati, Paolo Ciatti and James Wright. Online version: https://www.ems-ph.org/journals/of_article.php?jrn=rmi&doi=1302 Preprint: https://arxiv.org/abs/2011.13987
3. “Algebraic Stability of Oscillatory Integral Estimates: A Calculus for Uniform Estimates”, preprint. https://arxiv.org/abs/2104.12238
4. “Uniform Oscillatory Integral estimates for Convex Phases via Sublevel Set estimates”, preprint. https://arxiv.org/abs/2111.05395
5. “An L^{3/2} SL_2 Kakeya maximal inequality”, preprint., joint work with Terence Harris and Yumeng Ou https://hal.science/hal-04386684
PhD Thesis:
“The role of structure in oscillatory integral estimates” https://era.ed.ac.uk/handle/1842/39167
Teaching
In the Fall 2022 semester I taught MATH 1410 Calculus, Part II and MATH 6440 Partial Differential Equations.
In the Spring 2023 semester I taught MATH 4200 Ordinary Differential Equations.
In the Fall 2023 semester I taught MATH 1400 Calculus, Part I and MATH 3600 Advanced Calculus.
In the Spring 2024 semester I am teaching MATH 3130 Computational Linear Algebra.