I’m interested in the study of the partial differential equations (PDE) at the heart of general relativity: the Einstein equations. Solving them gives the geometrical structure of the space-time we live in.
From a mathematical point of view, the Einstein equations are a system of non-linear second order PDEs. From the seminal work of Choquet-Bruhat in the 50’s tackling local well-posedness to the work of Christodoulou and Klainerman in the 90’s which proved the non-linear stability of the Minkowski space-time, the study of the Einstein equations has produced a wealth of literature.
In the context of my PhD, I study high-frequency solutions to the Einstein vacuum equations. Those special solutions occur naturally from the study of backreaction for the Einstein equations, which was initiated by Isaacson and Burnett in the late 60’s and 80’s. They also describe the propagation of gravitational waves in a non-linear context.
Publications and preprints
4. High-frequency solutions to the constraint equations. June 2022, arXiv:2206.13062.
3. High-frequency solutions to the Einstein vacuum equations: local existence in generalised wave gauge. June 2022, arXiv:2206.12318.
2. Global existence of high-frequency solutions to a semi-linear wave equation with a null structure. September 2021, arXiv:2109.15204, accepted in Asymptotic Analysis.
1. Einstein vacuum equations with 𝕌(1) symmetry in an elliptic gauge: local well-posedness and blow-up criterium. January 2021, arXiv:2101.09093, submitted.
Articles 2,3 and 4 of this list constitutes my PhD thesis.
Seminars and talks
- Séminaire EDP (Université Rennes 1, IRMAR, November 2022)
- Mathematical GR and Hyperbolic PDE Seminar (Columbia, 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)
- 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 relativité (Sorbonne Université, LJLL, September 2020)
- Séminaire des doctorants ANH et ANEDP (Orsay, LMO, November 2019)