Uniruled symplectic manifolds

Dusa McDuff

A symplectic manifold is said to be uniruled if it has a nontrivial
genus zero Gromov-Witten invariant with a point among its constraints.
I shall sketch a proof that every symplectic manifold with a Hamiltonian
S1 action is uniruled.  The main tools are the Seidel representation of
the fundamental group of the Hamiltonian group in quantum cohomology and
the decomposition rule for relative Gromov-Witten invariants.
I will try to make the talk accessible to those who do not know much
symplectic geomery.