Séminaire hybride à l'Université McGill ou Zoom.

We exploit the structure of geometric graphs on Riemannian manifolds to analyze strategic dynamic graphs at the limit, when the number of nodes tends to infinity. This framework allows to preserve intrinsic geometrical information about the limiting graph structure, such as the Ollivier curvature. After introducing the setting, we derive a mean field game system, which models a strategic equilibrium between the nodes. It has the usual structure with the distinction of being set on a manifold. Finally, we establish existence and uniqueness of solutions to the system when the Hamiltonian is quadratic for a class of non-necessarily compact Riemannian manifolds, referred to as manifolds of bounded geometry.

Bio: Charles Bertucci is a CNRS Researcher in Mathematics at the Applied Mathematics Department of École Polytechnique, Palaiseau, France. He defended his thesis on December 11, 2018, and his Habilitation à Diriger les Recherches in June 2022.

Matthias Rakotomalala is a Third-year Ph.D. student at the Applied Mathematics Department of École Polytechnique, Palaiseau, under the supervision of Charles Bertucci.