  We show that any two birational projective Calabi-Yau manifolds have
isomorphic small quantum cohomology algebras after a certain change of Novikov
rings. The key tool used is a version of an algebra called symplectic
cohomology, which is constructed using Hamiltonian Floer cohomology. Morally,
the idea of the proof is to show that both small quantum products are identical
deformations of symplectic cohomology of some common open affine subspace. Part
of the proof uses the fact that subvarieties of positive codimension are stably
displaceable.
