Many-particle systems exhibit random fluctuations around their macroscopic behaviour. Fluctuating hydrodynamics seeks stochastic continuum equations describing these mesoscopic fluctuations. Such models arise in fluids, interacting diffusions, active matter, and related systems, but are often mathematically singular due to rough noise, nonlinear effects, and subtle notions of solution.

Recent progress has begun to make nonlinear models such as the Dean–Kawasaki equation and Landau–Lifshitz-type stochastic fluctuating hydrodynamics accessible to rigorous analysis.

The aim of the programme is to consolidate this emerging field and bring together researchers in probability, analysis, and related areas, with a focus on particle-to-SPDE limits, geometric extensions, stochastic transport, and random dynamical systems. The programme will feature a summer school and a workshop, complemented by seminars and collaborative research sessions.