Several structural equations from physics describe systems composed of a large number of interacting particles. These equations play a role in a wide number of fields (kinetic theory of gases, population dynamics, economics, etc…). To understand their large scale behavior by taking some suitable scaling limit is a well-known scientific challenge which has generated an intense research activity in the past decades, laying at the intersection between probability theory and PDEs.

This conference will focus on the mathematical investigation of such particle systems and on fundamental tools which are currently developed for their study, in particular: functional inequalities, and optimal transport, which both find applications in several domains of applied mathematics. Our aim is to foster contacts between specialists of the varied areas of probability and PDEs that are connected to these topics, in order to develop new methods and applications.