The purpose of this short article is to prove a product formula relating the log Gromov-Witten invariants of V×W with those of V and W in the case the log structure on V is trivial.

For ordinary flops, the correspondence defined by the graph closure is shown to give equivalence of Chow motives and to preserve the Poincaré pairing. In the case of simple ordinary flops, this correspondence preserves the big quantum cohomology ring after an analytic continuation over the extended Kähler moduli space. For Mukai flops, it is shown that the birational map for the local models is deformation equivalent to isomorphisms. This implies that the birational map induces isomorphisms on the full quantum rings and all the quantum corrections attached to the extremal ray vanish.

This an expository article on Givental's axiomatic Gromov--Witten theory and some of its applications.