The quantum equivariant cohomology of toric manifolds through mirror   symmetry
  Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten invariants of the target manifold. 
J.M. Baptista