This workshop will focus on two topics:

• Particle systems and their continuous limits,

• Nonlinear and, particularly, dispersive partial differential equations (PDEs).

The problem of hydrodynamic limits of particle systems is to rigorously derive macroscopic models, such as the fundamental PDEs of fluid mechanics, from a microscopic description of matter, whether molecular dynamics, interacting particle systems, or kinetic theory of gases. Raised by Hilbert in his sixth problem, this question has captured the attention of the mathematical community working in different areas across probability, analysis, and mathematical physics.

Nonlinear dispersive PDEs are omnipresent in applications wherever dispersion dominates dissipation, e.g., in the theory of water waves, nonlinear optics, Bose-Einstein condensates and plasma physics. The mathematical description of their solutions is challenging since it has to cover a vast array of phenomena as particle-like stable structures known as solitons, zones of rapid modulated oscillations as in the semiclassical limit of quantum mechanics known as dispersive shock waves and even a loss of regularity in finite time known as a blow-up (leading for instance to the destruction of optical fibers). Interestingly many of these equations are either completely integrable or in the vicinity of integrable structures. This allows the application of powerful tools from the theory of integrable systems leading to exact solutions for multi-solitons and an asymptotic description of dispersive shock waves and blow-up as well as the long-time behavior of the solutions, for instance soliton resolution. The combination of methods from the analysis of PDEs and the theory of integrable systems has led to recent breakthroughs.

The above two topics have a strong overlap in several respects: Concerning application fields, both kinetic models and dispersive equations are important models for quantum systems and plasma physics, e.g. On the methodological level, continuum and macroscopic limits have been a focus of intense research in both fields. Therefore, this workshop will bring these two communities into closer contact.