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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 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

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 will be responsible for teaching MATH 1410 Calculus, Part II and MATH 6440 Partial Differential Equations. Details will appear later.