Vortices and quantum Kirwan maps

The Vortex Seminar will consist of a minicourse in two parts (on Tuesday and Wednesday)

Given a Hamiltonian Lie group action on a symplectic manifold, the
Kirwan map is a natural ring homomorphism from the equivariant
cohomology of the manifold to the cohomology of the symplectic
quotient. By counting symplectic vortices over the plane, one
obtains a quantum deformation of this homomorphism. The map relates
the equivariant Gromov-Witten theory of the symplectic manifold with
the Gromov-Witten theory of the symplectic quotient.
On Tuesday, I will give some geometric background on the Kirwan map,
vortices and Gromov-Witten theory, and motivate the construction of a
quantization of the Kirwan map. On Wednesday, I will discuss a
relevant bubbling result, Fredholm theory, and decay at infinity for
vortices over the plane.