Water Waves, Hamiltonian Systems and Cauchy Integrals

I will speak today about a classical fluid dynamical problem involving a free surface, the problem known as water waves. The results I want to describe are simply the derivation of a formalism that arises in posing the problem. This consists in writing the equations of motion as a Hamiltonian system. In doing this, several interesting questions arise, which are associated with Laplace’s equation on plane domains. I am not reporting on analytical results, rather this talk should be taken as a description of a point of view, or a set of coordinates that have a certain elegance.