Diff. Geom, Math. Phys., PDE Seminar: Patrick Gerard

The cubic Szegö equation is an Hamiltonian evolution on periodic functions with nonnegative Fourier modes, arising as a normal form for the large time behavior of a nonlinear wave equation on the circle. It defines a flow on every Sobolev space with enough regularity. In this talk, I will give the main arguments for the proof of the following theorem. The trajectories of the cubic Szegö equation are almost periodic in the Sobolev energy space, but are generically unbounded in every more regular Sobolev space.This is a joint work with Sandrine Grellier and Zaher Hani.