Research

Broadly, I am interested in partial differential equations arising in general relativity and mathematical physics. I am particularly interested in nonlinear wave equations, the geometry and physics of asymptotic structures of spacetimes and fields, scattering theory, and the low-regularity properties of hyperbolic and dispersive PDEs. More recently I have also studied the equations of so-called Carrollian fluids.

Publications

Papers

1. Controlled regularity at future null infinity from past asymptotic initial data: the wave equation (with J. Marajh and J. A. Valiente Kroon).
   Submitted (2025).
   arXiv:2508.04690, 30 pages.
2. Global finite energy solutions of the Maxwell-scalar field system on the Einstein cylinder (with J.-P. Nicolas).
   Submitted (2025).
   arXiv:2507.16750, 46 pages.
3. One-dimensional Carrollian fluids III: global existence and weak continuity in $L^{\mathrm{\infty }}$ (with P. M. Petropoulos and S. Schulz).
   Journal of the London Mathematical Society 111 (6), e70186 (2025).
   arXiv:2407.05972, 31 pages.
4. One-dimensional Carrollian fluids II: $C^1$ blow-up criteria (with N. Athanasiou, P. M. Petropoulos, and S. Schulz).
   Journal of the London Mathematical Society, to appear.
   arXiv:2407.05971, 24 pages.
5. One-dimensional Carrollian fluids I: Carroll–Galilei duality (with N. Athanasiou, P. M. Petropoulos, and S. Schulz).
   Journal of High Energy Physics (JHEP) 11 (2024) 012.
   arXiv:2407.05962, 23 pages.
6. Wave map null form estimates via Peter–Weyl theory.
   Journal of Functional Analysis 289 (6), 111040 (2025).
   arXiv:2307.13052, 36 pages.
7. Controlled regularity at future null infinity from past asymptotic initial data: massless fields (with J. A. Valiente Kroon).
   Submitted (2023).
   arXiv:2304.08270, 42 pages.
8. Conformal scattering of Maxwell potentials (with J.-P. Nicolas).
   Annales de l'Institut Fourier, online first.
   arXiv:2211.14579, 48 pages.
9. Large data decay of Yang–Mills–Higgs fields on Minkowski and de Sitter spacetimes.
   Journal of Mathematical Physics 60 (12), 121504 (2019).
   arXiv:1902.08519, 22 pages.
10. Conformal scattering of the Maxwell-scalar field system on de Sitter space.
    Journal of Hyperbolic Differential Equations 16 (04), 743-791 (2019). arXiv:1809.01559, 39 pages.

Proceedings

1. Introduction: At the interface of asymptotics, conformal methods, and analysis in general relativity (with J. A. Valiente Kroon).
   Philosophical Transactions of the Royal Society A 382:20230048 (2024).
   
2. Scattering of Maxwell potentials on curved spacetimes.
   Ghent Methusalem Colloquium: Extended Abstracts 21/22, pp. 57-64 (2024).
   arXiv:2307.08398, 6 pages.

Edited Volumes

1. At the interface of asymptotics, conformal methods and analysis in general relativity (with J. A. Valiente Kroon).
   Philosophical Transactions of the Royal Society A 382 (2267) (2024).
   
   Proceedings for the conference of the same title, which took place at the Royal Society in London on 9–10 May 2023.

PhD Thesis

• Conformal scattering and analysis of asymptotic properties of gauge theories in general relativity. Oxford University Research Archive (2020).

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