Interview with Pierre Cardaliaguet, invited speaker at ICM2022

Link to the virtual ICM 2022 talks

What is your field of research?

I work in applied mathematics, especially on problems at the interface between PDEs, optimization, optimal control, and game theory. This work is usually stimulated by economics questions.

Are there place or encounters that were decisive in your career? Or findings that had a profound effect on the way you do mathematics?

I find it difficult to name any particular meeting because, as for most of us, my scientific practice is the fruit of a great many encounters and interactions. On the other hand, I would like to mention a particular place, the Ceremade, where I did my PhD, took my first research steps and to which I returned after ten (very happy) years or so at the University of Brest. The Ceremade is a rather singular place in France, which covers the essentials of applied mathematics, enriched by multiples interactions with the economic and industrial world. Its relatively modest size and the closeness of the intellectual interests of its members encourage discussion and the exchange of ideas. My work is imbued with this atmosphere: I owe it a lot.

Have you already decided what you are going to talk about at ICM2022?

My invitation to the ICM is a joint one with François Delarue (University of the Côte d'Azur). So, obviously, we’re going to talk about the work we have done together, in collaboration with J-M Lasry and P. L. Lions, on models of mean field games, in which we show, under certain conditions, the existence and uniqueness of  a solution to a partial differential equation in a measure space (the “master equation”); we also explain that the existence of this solution means a certain convergence of some N-player games on a medium-field game when N tends to infinity, as well as a propagation of chaos property for optimal trajectories.