My main research area lies between probability theory, differential geometry and mathematical physics. It consists in studying the links between the geometry of pseudo-Riemannian manifolds, especially Lorentzian manifolds, and the behavior of random curves, such as Brownian motions, drawn on these manifolds.

In my Ph.D [2], I studied in detail the (long time) asymptotic behavior of a relativistic Brownian motion in a large class of Lorentzian manifolds : Robertson-Walker spacetimes. The Brownian motion in question takes values in the unitary tangent bundle of the underlying manifold, its infinitesimal generator is a perturbation of the geodesic flow by the vertical Laplacian. I established precise links between the asymptotic behavior of Brownian paths and the asymptotic behavior of light-like geodesics of the manifolds [4]. I also made some connections between the Poisson boundary of the process and the causal boundary of the underlying manifolds [3, 4]. I am continuing my research in this area trying to determine the Poisson boundary of the Brownian motion in some geometrical situations not considered in my thesis.

I also am interested in various issues of mathematical physics involving stochastic processes in the context of the theory of relativity. With Jacques Franchi, we have thus established in [1, 2] a central limit theorem for a large class of Minkowskian diffusions that contains most of the examples of the physics literature. One of my research goal is to extend some results of [1] in the framework of general relativity [5]. Among my other projects is the study of discrete models of the theory of gravitation and their links with the concept of relativistic Brownian motion. 

Since my arrival in the very dynamic team of Mathematical Physics of University of Geneva, I also shared some of the interests of my colleagues, in particular I am interested in problems of harmonic analysis and Potential Theory in sets of irregular boundary.