I am interested in symplectic geometry and Hamiltonian PDEs. More precisely, I study rigidity properties of particular types of symplectic diffeomorphisms such as Hamiltonian flows. The main tools that I use are generating functions and symplectic capacities. I am also interested in the effect that these properties have in infinite dimension on flows of Hamiltonian PDEs, in particular, on flows which can be uniformly approximated by finite dimensional Hamiltonian diffeomorphisms.
