Order and Randomness in Partial Differential Equations

The program focuses on three separate, yet connected, areas: fluid motion, integrable systems and stochastic partial differential equations.

Generally, it’s impossible to solve nonlinear partial differential equations explicitly. However, certain nonlinear equations have remarkable properties which allow for explicit solutions or at least for the equations to be solved using only linear operations. These equations are called completely integrable and can be seen as generalisations of integrable systems in classical mechanics. Many examples of integrable systems appear specifically in the context of fluid mechanics and thus allows for a precise description of the fluid motion in certain cases. On the other hand, one of the hallmarks of fluid motions is turbulence, in which the fluid flow is chaotic, and one can only hope to get a good grasp by studying statistical properties of the solutions rather than individual solution trajectories.

The program will promote cross-fertilization between these different areas which will hopefully lead to new ideas and progress.

During the program, there will be two workshops with thematically focused talks:

September 11 – 15, 2023: Water Waves and Integrable Systems

Organizers: Jean-Claude Saut, Catherine Sulem and Erik Wahlén.

Dedicated to the memory of Thomas Kappeler.

September 4 – 8: ​Mini courses by Massimiliano Berti, SISSA and Patrick Gérard, Université Paris-Saclay. Dates and speakers for mini courses are preliminary.

November 27 – December 1, 2023: Stochastic Flows

Organizers: Helge Holden, Susanne Solem and José A. Carrillo.

November 20 – 24: Mini courses by José A. Carrillo, University of Oxford and Sergei Kuksin, IMJ-PRG.