Webpage of R.L.

I am a postdoctoral fellow at École des Ponts (CERMICS), affiliated with the MATHERIALS team at INRIA, under the supervision of Virginie Ehrlacher, Tony Lelièvre, and Julien Reygner. My research is supported by the HighLEAP ERC grant, led by Virginie Ehrlacher.

I completed my PhD at Université Paris-Dauphine under the supervision of Mathieu Lewin, where I was a member of the MDFT ERC grant team. Prior to that, I studied at École Polytechnique and École Normale Supérieure de Paris-Saclay.

You can contact me at firstname.name@enpc.fr.

Research interests

1. Theory and numerics of optimal transport especially its multimarginal extension as it appears in density functional theory in quantum chemistry. Here is a partial overview of some contributions of mine on this subject:
   • In [1], I proved that the Kantorovich potential for the multimarginal optimal transport with Coulomb cost is a superharmonic function, which can therefore be expressed as the electrostatic potential generated by a charge density. I then utilise this parametrisation to numerically solve the multimarginal optimal transport problem by discretising this charge density and solving the Kantorovich dual using classical optimisation and Monte Carlo-type methods.
   • In [2], I proved a conjecture regarding the asymptotics of the Kantorovich potential for repulsive transportation costs as commonly encountered in physics. This conjecture can be interpreted as a classical ionization conjecture for the strictly-correlated electrons system.
   • At the present time, I am working (with Luca Nenna & Virginie Ehrlacher) on several questions, among which the regularity of the multimarginal optimal transport with general costs (and implicitely on the existence of Monge transport maps in the multimarginal setting), as well as on the moment-constrained optimal transport and other numerical methods.
2. Study of classical (and continuous) statistical physics systems such as Coulomb and Riesz gases, with a particular focus on the existence of the thermodynamic limit and phase transitions. Here is a contribution of mine on this subject:
   • In [3], I showed numerical evidences that the one-dimensional Riesz gases exhibit phase transitions with respect the temperature in the long-range interaction regime, more precisely for the non-singular Riesz pair potential with exponent −1 ≤ s ≤ 0.
3. Model order reduction techniques for high-dimensional stochastic differential equations.
   • In the forthcoming paper [4] in collaboration with Virginie Ehrlacher, Tony Lelièvre and Julien Reygner, we explain how to build projection of stochastic differential equations onto submanifolds of ℝ^d and develop numerical schemes for these objects that remain exactly onto the submanifold.

Publications

Teaching

I was a teaching assistant at Université Paris-Dauphine. Some personal material for the fourth-year course Analyse numérique: évolution of Gabriel Turinici are available, namely a practical work (.pdf, .ipynb) on the numerical integration of (stiff) ordinary differential equations. Although the material is fairly standard, I did manage to find an example of a differential equation y′ = f(t, y) for a non-Lipschitz dynamics f which nevertheless admits an unique solution, and for which standard numerical schemes fail to converge. Another practical work (.pdf, .ipynb) that deals with numerical integration of stochastic differential equations — with a somewhat long additional exercise that includes a remarkable result from random matrix theory and statistical physics.

For the course Analyse des équations aux dérivées partielles for first year students of Ecole des Ponts, here are some (sketchy) corrections.