Title: Moment maps, almost complex structures and quasimorphisms

Abstract: Given any symplectic manifold of finite volume, we use the action of its Hamiltonian group on the space of compatible almost complex structures to construct a non-trivial quasimorphism (on the universal cover of the group). As an application we show that two norms on \tilde{Ham} are unbounded. Key notions in the construction include Weinstein's Action homomorphism, the Donaldson-Fujiki moment map and bounded cocycles given by integration over geodesic triangles.