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.
I an interested in Harmonic Analysis, and in particular, I have recently been considering uniform oscillatory integral estimates and their relation to uniform sublevel set estimates in the presence of additional qualitative, geometric structural assumptions.
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
“The role of structure in oscillatory integral estimates” https://era.ed.ac.uk/handle/1842/39167
In the Fall 2022 semester I will be responsible for teaching MATH 1410 Calculus, Part II and MATH 6440 Partial Differential Equations. Details will appear later.