I will briefly describe how the construction of a global Kuranishi chart for moduli
spaces of stable pseudoholomorphic maps allows for a straightforward definition of
sympletic GW invariants, including gravitational descendants. Subsequently, I will
describe how to extend this to the equivariant setting and sketch the proof of a
localisation formula for the equivariant GW invariants of a Hamiltonian torus
manifold. This is partially joint work with Mohan Swaminathan.
