Summer School on Wave Turbulence

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