  The main result of this note is that every closed Hamiltonian S^1 manifold is
uniruled, i.e. it has a nonzero Gromov--Witten invariant one of whose
constraints is a point. The proof uses the Seidel representation of \pi_1 of
the Hamiltonian group in the small quantum homology of M as well as the blow up
technique recently introduced by Hu, Li and Ruan. It applies more generally to
manifolds that have a loop of Hamiltonian symplectomorphisms with a
nondegenerate fixed maximum. Some consequences for Hofer geometry are explored.
An appendix discusses the structure of the quantum homology ring of uniruled
manifolds.
