Project Summary

The project is organized around the interaction between probability theory and analysis of partial differential equations, with a particular focus on the use of functional inequalities as a structuring tool, to solve open problems in applied mathematics. We are interested in several broad areas of mathematics, including interacting particle systems, analysis of evolution equations and their long-time behavior, mean-field dynamics, stability of functional inequalities, and numerical algorithms. We work on both continuous models (diffusion processes, parabolic PDE…) and discrete ones (particle systems on graphs, random walks), as well as situations that mix aspects of both (discretizations of PDE, jump processes, Piecewise Deterministic Markov Processes). The concrete problems we study are mostly mathematical in nature, but motivations come from a broad range of fields, including physics, biology, computer science, information theory and data sciences. We are interested in mathematical models for real-world problems, as well as in the development and rigorous analysis of numerical algorithm