Interacting particles, PDEs and applications (04/26 --> 12/26)

Many complex systems in physics, biology, and the social sciences consist of a large number of interacting agents whose emergent behavior can often be described by nonlinear PDEs. Over recent decades, significant progress has been made in understanding the rigorous derivation of these continuum models from interacting particle systems, as well as in analyzing the rich mathematical structures underlying the equations involved at both scales. The developments include mean-field limits, hydrodynamic limits, kinetic and fluid equations, non-local PDEs, degenerate diffusion and cross-diffusion systems, branching processes, and stochastic models of collective behavior. The thematic semester Interacting Particles, PDEs and Applications (IMT, Spring-Autumn 2026) aims to strengthen connections between communities developing these tools—probabilists, analysts, mathematical physicists, and specialists in mathematical biology. The semester combines a research school, two international conferences and an online seminar running throughout the semester. This will offer a coherent framework to explore the links between microscopic stochastic models and macroscopic continuum equations, from the theoretical mathematical analysis to the practical applications, in particular in the context of life sciences. It will provide a platform for collaboration, interdisciplinary exchange, and training of young researchers.

All onsite events take place at the Institute of Mathematics of Toulouse (IMT): Google Map link

Events:

• MINT summer school Particle systems and PDEs
• Conference Particle systems and PDEs XIV
• Conference PDEs under pressure and applications in life science
• Online seminar series Interacting particles, PDEs and applications

Coordinators:

• Marina Ferreira (CNRS and Université de Toulouse)
• Francis Filbet (Université de Toulouse)
• Pierre Gervais (Université de Toulouse)
• Ariane Trescases (CNRS and Université de Toulouse)

This semester has received the support of the International Center of Mathematics and Computer Science in Toulouse (CIMI), the MINT graduate school, CNRS, Université de Toulouse, Institut de Mathématiques de Toulouse, Institut Camille Jordan, Universidad de Lisboa, Universidad do Minho, the ANR grant MBAP-P, the PEPR grant PREMMOVE, the FCT grants UIDB/04459/2020 and UIDP/04459/2020 and UID/00013/2025 and the RT Math Bio Santé