Research

I’m interested in the study of the partial differential equations (PDE) at the heart 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.

5.   Initial data for Minkowski stability with arbitrary decay, with Allen Juntao Fang and Jérémie Szeftel, 2024.

4.   High-frequency solutions to the constraint equations. Commun. Math. Phys, 402(1):97-140, 2023.

3.   Geometric optics approximation for the Einstein vacuum equations. Commun. Math. Phys, 402(3):3109-3200, 2023.

2.   Global existence of high-frequency solutions to a semi-linear wave equation with a null structureAsymptotic 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 criteriumJournal 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

1.   Geometric optics approximation for the Einstein vacuum equations. Séminaire Laurent Schwartz — EDP et applications, Exposé no. 7, 12 p. (2022-2023)

 

Seminars & conferences

2024

2023

2022

2021

2020

  • Groupe de lecture en relativité (Sorbonne Université, LJLL, September 2020)

2019