## Four Hour Short Course By:

- Raffaele Ferrari MIT
- Isabelle Gallagher Ecole Normale Supérieure
- Jacques Vanneste University of Edinburgh
- Hendrik Weber University of Münster
- Miguel Escobedo Universidad del País Vasco

MIT, Cambridge | July 24-28, 2023

Sponsored by the Simons Collaboration on Wave Turbulence

- Raffaele Ferrari MIT
- Isabelle Gallagher Ecole Normale Supérieure
- Jacques Vanneste University of Edinburgh
- Hendrik Weber University of Münster
- Miguel Escobedo Universidad del País Vasco

This summer school will introduce participants to several topics in partial differential equations at the intersection of mathematical analysis and physics through five lecture series, covering both theory and application. There are two main themes: kinetic equations describing large systems of interacting waves or particles and singular stochastic PDE. The target audience is graduate students and early-career researchers.

**Topics in kinetic equations:**

- The well-posedness and asymptotic dynamics for solutions to the 4- and 3-wave kinetic equations
- The derivation of the Boltzmann equation from a system of hard spheres and the study of fluctuations / large deviations around this limit equation
- How turbulence on different scales affects the global circulation of the ocean, and how turbulent theories are used to represent ocean turbulence in climate models
- Wave scattering and redistribution of wave energy in wavenumber space in relation to atmospheric and oceanic wave propagation in turbulent flows

**Topics in singular stochastic PDE:**

- Review of systematic solution theories (e.g., regularity structures and paracontrolled distributions) for local existence of solutions
- Question of global existence / a priori bounds for solutions
- Equations in mathematical physics, such as KPZ and the stochastic quantization equations for the 3D $\Phi^4$ and Yang Mills measures

- Gigliola Staffilani MIT
- Andrea Nahmod University of Massachusetts at Amherst
- Zaher Hani University of Michigan

Rosalee Zammuto summerschoolonwaveturbulence@mit.edu