Abstract:
The area of infinite-dimensional dynamical systems (mostly governed by PDEs) knows many instances where symplectic and advanced Hamiltonian system methods are applicable, be it rigorous or formal. Prominent examples include KAM theory in infinite dimensions, integrable systems, growth of Sobolev norms/non-squeezing for equations such as KdV, Marsden-Weinstein reduction with respect to symmetry groups, etc. It is the purpose of this project to develop two of those promising topics further.