The Bézout Research Federation is a CNRS research unit (FR3522) created in 2011, with the same scientific and institutional perimeter as the Bézout Labex, its main source of funding. Its referent institutions are CNRS, ENPC, Université Gustave Eiffel, and UPEC.
In particular, the Bézout Federation fosters inter-laboratory, inter-disciplinary, and regional research in mathematics and computer science. It identifies the union of the three laboratories CERMICS, LAMA, and LIGM from the CNRS side.
The Bézout Research Federation is a member of the DIM Math Innov, a network of many laboratories and institutions in mathematical sciences in the Paris area. The other members are Institut Henri Poincaré, Fondation Sciences Mathématiques de Paris, Fondation Mathématique Jacques Hadamard, and Paris-Seine.
PEPS JCJC 2022-2023 (Amaury Hayat – CERMICS) : This project deals with the stabilization of systems that are described by the evolution of a density and a velocity. These systems, influenced by external forces, are found in many physical phenomena. The project aims, on one hand, to explore the robustness of the obtained controls with respect to the system’s geometry and a possible viscosity. On the other hand, it aims of developing general methods for the stabilization of such systems. This project has been conducted with many co-authors and has resulted in three submitted papers and three papers currently in preparation.
IEA SHYSTRA 2022-2023 (Amaury Hayat – CERMICS) : This is a collaboration with Benedetto Piccoli (Rutgers University Camden) and Shengquan Xiang (EPFL, now Beijing University). The goal is to study the stabilization of hyperbolic systems with discontinuous solutions using pointwise controls. This system models, for instance, congested road traffic that we would like to stabilize (i.e. eliminate stop-and-go waves) using some autonomous vehicles. Since the obtained solutions are neither regular nor entropic, this requires new mathematical tools.