210129 Marine Fontaine

By complexifying a Hamiltonian system one obtains dynamics on a holomorphic symplectic manifold. To invert this construction we present a theory of real forms which not only recovers the original system but also yields different real Hamiltonian systems which share the same complexification. In this talk I will explain the notion of real form for a symplectic manifold, more generally, for a Poisson manifold and will discuss their applications to integrable Hamiltonian systems. This is based on joint work with P. Arathoon.