Georgia Institute of Technology School of Mathematics | Georgia Institute of Technology | Atlanta, GA

In the world of Hamiltonian partial differential equations, complete integrability is often associated to rare and peaceful dynamics, while wave turbulence rather refers to more chaotic dynamics. In this talk I will first try to give an idea of these different notions. Then I will  discuss the example of the cubic Szegö equation, a nonlinear wave toy model which surprisingly displays both properties. The key is a Lax pair structure involving Hankel operators from classical analysis, leading to the inversion of large ill-conditioned matrices. .