Research

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, accepted in Journal of Hyperbolic Differential Equations.

Articles 2,3 and 4 of this list constitutes my PhD thesis.

Seminars and talks