People A-Z

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JohnGreen

Research Interests

Harmonic analysis, Real Analysis

Biographical Statement

I am a PhD student interested in real and harmonic analysis working under the supervision of Jim Wright. I am particularly interested in oscillatory integral estimates with uniformity within a class of functions, and the relation between such estimates and the corresponding sublevel set estimates. Recently, I have been thinking about ways of proving oscillatory integral estimates from the corresponding sublevel set estimates in the presence of certain 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. (to appear in print), 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

Education Background

MMath University of Warwick (2018)

Jim Wright