Central extensions of the group of Hamiltonian Diffeomorphisms

I will start by describing the universal central extension of the Lie algebra of Hamiltonian vector fields. This gives one a description of the Lie algebra cohomology classes in degree 2 with values in the 1-dimensional trivial representation. Not all of these classes integrate to the group level. By studying the action of the Hamiltonian diffeomorphism group on suitable spaces of closed embedded submanifolds, we find a lattice of cohomology classes that do.
(This is joint work with Cornelia Vizman.)