Projet LiBERA (Horizon Europe, appel à projets 2023)
Action : Staff Exchanges
Panel : Mathematics
Statut du projet : SIGNED

This SE aims at addressing a number of challenging mathematical problems related to stochastic interacting systems, with particular emphasis on the regularity properties of the solutions, their limiting behaviour and numerical computation. The equations we analyse arise from the modelisation of real-world phenomena in several fields of application, including spiking neural systems, hydrodynamics and financial/energy markets, and share nonlinearity as a common underlying trait. Critically, nonlinearity intertwines with other relevant features that include: low regularity of the coefficients, noise degeneracy, jump-diffusion dynamics, and high-dimensionality. The study of stochastic interacting systems is highly multidisciplinary from a two-fold perspective. On one hand, they have become a widespread modelling tool in a variety of applications. For example, they are used to model human neuron interfaces, particle systems, but also interacting agents in economics and finance, in relation to managing risk and decentralised production of renewable energy. On the other hand, the set of mathematical and computational tools needed to reach a holistic understanding of stochastic systems is very vast: ranging from stochastic (partial) differential equations, random measures, rough paths, gradient flows in metric measure spaces, numerical probability and computer simulation. We provide a team of experts that analyse stochastic systems integrating several approaches and techniques. The complementary expertise across the network, together with the consolidated experience and excellence of the key participants in their research areas, places our network in the privileged position to make relevant contributions across interconnected research fields, and to contribute to the training of the early career researchers involved in the project in an exciting field of pure and applied mathematics, with the possibility of boosting their careers in both academic and non-academic sectors.

Mots clés : stochastic partial differential equations, interacting particle systems, kinetic pdes, numerical probability, stochastic control, langevin equations, mean field games, mckean vlasov, hawkes process

Participants :
- Université d'Uppsala (Suède) — Partner, associated partner, Enseignement supérieur ou secondaire, subvention : 0.0 €
- Institut national de mathématiques pures et appliquées (Brésil) — Partner, associated partner, Enseignement supérieur ou secondaire, subvention : 0.0 €
- Université d'Édimbourg (Royaume-Uni) — Partner, associated partner, Enseignement supérieur ou secondaire, subvention : 0.0 €
- Université de Bologne (Italie) — Coordinator, beneficiary, Enseignement supérieur ou secondaire, subvention : 312800.0 €
- Mathematics Research Center (Mexique) — Partner, associated partner, Enseignement supérieur ou secondaire, subvention : 0.0 €
- Université Columbia (Etats-Unis) — Partner, associated partner, Enseignement supérieur ou secondaire, subvention : 0.0 €
- Université de l'Alberta (Canada) — Partner, associated partner, Enseignement supérieur ou secondaire, subvention : 0.0 €
- Électricité de France (France) — Partner, associated partner, Organismes privés (hors enseignement), subvention : 0.0 €
- Université de Padoue (Italie) — Partner, beneficiary, Enseignement supérieur ou secondaire, subvention : 151800.0 €
- École polytechnique fédérale de Lausanne (Suisse) — Partner, associated partner, Enseignement supérieur ou secondaire, subvention : 0.0 €
- Fundación Universitaria del Espinal (Colombie) — Partner, associated partner, Enseignement supérieur ou secondaire, subvention : 0.0 €
- London School of Economics and Political Science (Royaume-Uni) — Partner, associated partner, Enseignement supérieur ou secondaire, subvention : 0.0 €
- Arizona's Public Universities (Etats-Unis) — Partner, associated partner, Enseignement supérieur ou secondaire, subvention : 0.0 €
- Université Paris 1 - Panthéon Sorbonne (France) — Partner, beneficiary, Enseignement supérieur ou secondaire, subvention : 55200.0 €
- Federal University of Paraíba (Brésil) — Partner, associated partner, Enseignement supérieur ou secondaire, subvention : 0.0 €
- University College de Londres (Royaume-Uni) — Partner, associated partner, Enseignement supérieur ou secondaire, subvention : 0.0 €
- Coordinador independiente del sistema eléctrico nacional (Chili) — Partner, associated partner, Autres, subvention : 0.0 €
- Université de Ritsumeikan (Japon) — Partner, associated partner, Autres, subvention : 0.0 €
- Université Aalto (Finlande) — Partner, beneficiary, Enseignement supérieur ou secondaire, subvention : 124200.0 €
- Université de Tokyo (Japon) — Partner, associated partner, Enseignement supérieur ou secondaire, subvention : 0.0 €
- Université de Lisbonne (Portugal) — Partner, beneficiary, Enseignement supérieur ou secondaire, subvention : 280600.0 €
- Université libre de Bruxelles (Belgique) — Partner, associated partner, Enseignement supérieur ou secondaire, subvention : 0.0 €
- Université libre de Berlin (Allemagne) — Partner, associated partner, Enseignement supérieur ou secondaire, subvention : 0.0 €