Paris/Berkeley/Bonn/Zürich Analysis Seminar: Weak turbulence

Seminar | September 20 | 9:10-10 a.m. | 238 Sutardja Dai Hall

 Anne-Sophie de Suzzoni, École Polytechnique

 Department of Mathematics

Wave turbulence is the study of the evolution of the statistics of random waves. Weak turbulence corresponds to taking an equation, coming from hydrodynamics or quantum mechanics, which is weakly nonlinear (that is we let its nonlinearity go to zero in a certain regime). One aim of this talk is to present the first aspects of the theory of weak turbulence from a mathematical physics point of view, explain which intrinsically nonlinear behavior it describes, its link with resonances and the growth of Sobolev norms. We will then present some rigorous results and perspectives. One aim is to introduce the computational tool of Feynmann diagrams in this context, its relevance and importance in fully developing the mathematical study of weak turbulence.

We will discuss a joint work with Nikolay Tzvetkov and an ongoing project with Zaher Hani.