I will explain how Hamiltonian circle actions on non-compact symplectic manifolds give rise to generators and relations in the symplectic cohomology ring. In particular, if the Reeb flow at infinity arises from a Hamiltonian circle-action, then the symplectic cohomology is a quotient of quantum cohomology. For example this applies to negative line bundles. In the case of toric negative line bundles, this yields an explicit presentation of the quantum and symplectic cohomologies, and one obtains generators for the wrapped Fukaya category when the superpotential is a Morse function. A key ingredient is the open-closed string map and a generation criterion obtained in joint work with Ivan Smith.