Mathematics

I shall present a result obtained in collaboration with Luca Biasco and Jessica Massetti on the construction of invariant maximal tori for NLS equations with external parameters. Our strategy, which develops from the one proposed by Bourgain for a similar problem, allows us to recover the existing literature in a unified way and gives us a good insight on the very challenging problem of proving the existence of almost periodic solutions for the NLS equation without parameters. Time permitting I shall also show how our functional setting can be used in order to obtain Nekoroshev type esitmates for the stability of the NLS at zero.