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) To appear in Advances in Theoretical Mathematical Physics, 2024.
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).