I’m interested in the study of the partial differential equations at the heart of the theory of general relativity: the Einstein equations. My research is twofold:
- Construction of high-frequency solutions to the Einstein vacuum equations.
- Stability of black holes as solutions to the Einstein vacuum equations.
For these two programs, I’m interested in both the hyperbolic and elliptic aspects, i.e the evolution equations and the constraint equations.
Links to my collaborator’s 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).
Seminars & conferences
2025
- Séminaire de l’équipe EDP Analyse Numérique (Université Côte d’Azur, Nice, April 2025)
- Seminar on Mathematical General Relativity (Sorbonne Université, LJLL, March 2025)
2024
- Singularity formation for nonlinear PDEs (Cambridge University, September 2024)
- Mathematical GR and Hyperbolic PDE Seminar (Columbia University, June 2024)
- Séminaire de Géométrie (LMPT, Tours, May 2024)
- Vienna Relativity Seminar (University of Vienna, May 2024)
- Seminar of Differential Equations and Numerical Analysis (University of Crete, April 2024)
- Séminaire de l’équipe Analyse Numérique-EDP (LMO Orsay, April 2024)
- Séminaire Mathématique-Physique (IMB, Dijon, January 2024)
- Séminaire d’analyse (LMJL, Nantes, January 2024)
2023
- Séminaire de Physique Mathématique EDP (IMB, Bordeaux, December 2023)
- Greater Paris Postdocs in Mathematics Welcome Day (IHES, October 2023)
- Evolution Equations Workshop (IHES, October 2023)
- Séminaire Analyse & EDP (CY AGM, September 2023)
- Journées Jeunes EDPistes (Tours, March 2023)
- Gravity Initiative Seminar (Princeton University, February 2023)
- Séminaire du laboratoire (LMR, Reims, February 2023)
- London PDE Seminar (Imperial-UCL-Queen Mary, February 2023)
- Séminaire de physique mathématique (Institut Fourier, Grenoble, January 2023)
- Groupe de lecture en relativité (Sorbonne Université, LJLL, January 2023)
2022
- Séminaire Laurent Schwartz (CMLS-IHES, December 2022)
- Séminaire EDP (Université Rennes 1, IRMAR, November 2022)
- Mathematical GR and Hyperbolic PDE Seminar (Columbia University, May 2022)
- Topics in general relativity (WWU Münster, April 2022)
- HADES Seminar (Berkeley University, March 2022)
- Analysis & PDE Seminar (Stanford University, March 2022)
- Séminaire EDP et Physique mathématique (Université Sorbonne Paris Nord, LAGA, February 2022)
2021
- Vienna Relativity Seminar (University of Vienna, December 2021)
- Seminar on Mathematical General Relativity (Sorbonne Université, LJLL, December 2021)
- Séminaire des doctorants du CMAP et du CMLS (Ecole Polytechnique, February 2021)
- Groupe de travail en analyse du CMLS (Ecole Polytechnique, January 2021)
2020
- Groupe de lecture en relativité (Sorbonne Université, LJLL, September 2020)
2019
- Séminaire des doctorants ANH et ANEDP (Orsay, LMO, November 2019)