The Team : The Ambition project “CY Nonlinear Analysis” is a collective proposal from the research team in nonlinear analysis of the AGM Research Center in Mathematics (UMR CNRS 8088) of CY Cergy Paris University. This team gathers young and senior researchers, whose scientific expertise covers a broad spectrum of topics in geometric analysis, mathematical physics, partial differential equations and probability. The team is composed of :

• Charles Collot (CNRS Junior Researcher),
• Françoise Demengel (Professor),
• Philippe Gravejat (Professor),
• Emmanuel Hebey (Professor),
• Élisabeth Logak (Professor),
• Frank Merle (Professor),
• Christophe Prange (CNRS Junior Researcher)
• Marjolaine Puel (Professor),
• Nikolay Tzvetkov (Professor),
• Wei-Min Wang (CNRS Senior Researcher).

Scientific Goals : The main goal of this project is to consolidate the research activity of this team and to strengthen its international attractivity. On a scientific level, nonlinear analysis is an extremely active field in mathematics with significant applications to other mathematical domains like dynamical systems, geometry and probability, as well as to physics (in fluid mechanics, general relativity or quantum mechanics) or to economy. In the last decades, a long series of breakthroughs improved the understanding of the main issues: existence and regularity theories for general solutions, construction and stability of particular solutions, and classification problems. The team was involved in certain of these achievements. This understanding is however far from being complete, as no universal approach, that would be applicable to all equations, seems possible. This topic is thus nowadays an active and diverse domain of research. Part of the scientific program of the project will be devoted to the existence and regularity theories, either in a deterministic or in a random context. The focus will also be put on the qualitative analysis of the previously constructed solutions, by tackling issues like their asymptotic regimes, their regularity or their singularities, their asymptotic dynamics, possibly the classification of their behaviours or properties.

Organisation : The coordination of the project is handled by Philippe Gravejat. An inaugural workshop is planned to initiate the scientific program of the project. This workshop will be held at the Maison Internationale de la Recherche of CY Cergy Paris University next year. A concluding conference will be organized during Spring 2025.

A significant part of the budget will be devoted to the hiring of a three-year post-doctoral researcher. The successful candidate will be selected on the basis of his or her academic excellence in order to strengthen any scientific axis of the project. Following the usual calendar for similar hirings, this position is planned to be opened at the beginning of September 2022.