General relativity
Finite time singularity formation and asymptotic stability
Derivation of the nonlinear Schrödinger equation
Domain decomposition methods
Long-time existence problems on compact manifolds
Absorbing boundary conditions
Propagation/ reflection of singularities, smoothing effect
I defended my Habilitation thesis on October 8th 2012 (Univerité Paris 13). You can download my Habilitation thesis in .pdf.
Between October 2000 and April 2004, I have been doing a PhD on "Pseudodifferential and paradifferential calculus for the study of absorbing boundary conditions and qualitative properties of nonlinear PDE's" at Univerité Paris 13 under the guidance of Laurence Halpern. You can download my PhD thesis in .pdf.
Here is the proceeding of the talk I gave at ICM 2014 The resolution of the bounded L2 curvature conjecture in general relativity.