My primary research interests lie in the study of the partial differential equations at the heart of the theory of general relativity: the Einstein equations. I started by constructing high-frequency spacetimes in the context of the Burnett conjecture, and now also work on the black hole stability problem. For these two programs, I’m interested in both the hyperbolic and elliptic aspects, i.e the evolution equations and the constraint equations. More recently, I’ve started working on wave turbulence.
Links to my collaborators’ websites:
Articles & preprints
In reverse chronological order taking into account the first release on arXiv.
8. Wave turbulence for a semilinear Klein-Gordon system (with Anne-Sophie de Suzzoni and Annalaura Stingo) 2025.
7. Spacelike initial data for black hole stability (with Allen Juntao Fang and Jérémie Szeftel) To appear in Communications in Mathematical Physics, 2024.
6. The reverse Burnett conjecture for null dusts To appear in Annals of PDE, 2024.
5. Initial data for Minkowski stability with arbitrary decay (with Allen Juntao Fang and Jérémie Szeftel) Advances in Theoretical Mathematical Physics, 29(4):933-1043, 2025.
4. High-frequency solutions to the constraint equations Communications in Mathematical Physics, 402(1):97-140, 2023.
3. Geometric optics approximation for the Einstein vacuum equations Communications in Mathematical Physics, 402(3):3109-3200, 2023.
2. Global existence of high-frequency solutions to a semi-linear wave equation with a null structure Asymptotic Analysis, 131(3-4):541-582, 2023.
1. Einstein vacuum equations with 𝕌(1) symmetry in an elliptic gauge: local well-posedness and blow-up criterium Journal of Hyperbolic Differential Equations, 19(04):635-715, 2022.
Articles 2, 3 and 4 of this list constitute my PhD thesis, which starts with an introduction written in French.
Proceedings & surveys
2. Burnett’s conjecture in general relativity Recent advances in general relativity: an issue in memory of Yvonne Choquet-Bruhat, Comptes Rendus Mécanique, Volume 353, pp 455-476, 2025.
1. Geometric optics approximation for the Einstein vacuum equations Séminaire Laurent Schwartz — EDP et applications, Exposé no. 7, 12 p. (2022-2023).
Organization
- Conférence MARGAUx : EDP et Analyse Numérique en Nouvelle-Aquitaine, organized with Ludovic Godard-Cadillac and Victor Arnaiz Solorzano, three days conference from March 30th to April 1st 2026 at IMB, more information to come!
- Working Group on nonlinear PDEs, from 2025 onward, regular seminar taking place at IMB.
- Conference on Harmonic Analysis and Turbulence, organized with Aingeru Fernández Bertolin, Francesco Fanelli, David Lannes and Luis Vega, a three days conference on April 14th to 16th 2025 at IMB, more information on this page.
- Conférence Turbulent·e·s, organized with Anne-Sophie de Suzzoni, Guillaume Dubach and Annalaura Stingo, a two days conference on May 23rd and 24th 2024 at Ecole Polytechnique, more information on this page.
- Reading Group in General Relativity, from 2022 to 2024, monthly seminar taking place at LJLL (Sorbonne Université) and CMLS (École Polytechnique).