# On Hamiltonian Gromov-Witten theory for symplectic reductions

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In this talk, I will first review our work on defining a new quantum deformation for the (Chen-Ruan) cohomology ring of a symplectic reduction. Then I will explain the relation between this quantum deformation and the well-known quantum cohomology ring. Our construction is based on the study of moduli spaces of symplectic vortices with proper metrics. This is a joint project with B. Chen and B. Wang.