More recently, I worked with Patrick Ciarlet, Serge Nicaise and Thierry Horsin on the existence of solutions to Maxwell's equations in a chiral medium, with an application to exact boundary controllability.

During my postdoctoral stay at the Centro de Modelamiento Matemático (UMI 2807 CNRS-Universidad de Chile, Santiago, Chile) and in collaboration with Takéo Takahashi, I studied fluid-structure interaction problems and, more particularly, the convergence of a numerical method based on a finite element discretisation, combined with the method of characteristics, of an Arbitrary Lagrangian Eulerian (ALE) formulation of a viscous fluid/rigid body interaction problem. The major difficulties in such an analysis arise from the coupling between the equations of the fluid and those of the structure and from the free boundary of the domain.

I also work, notably with Mathieu Lewin and Éric Séré, on the development of mathematically sound computational methods in relativistic quantum chemistry, which takes into account the fine effects encountered by the core electrons in heavy atoms. I am more particularly interested in the implementation and study of the behavior (convergence, discretization issues...) of new algorithms based on previous works from members of the project ACCQUAREL, for models of the Dirac-Hartree-Fock type. These models lead to difficult issues due to the lack of lower bound on the (continuous) spectrum of the Dirac operator. In particular, the considered energies are not bounded from below, a property which forbids to use the usual methods devoted to the non-relativistic case.