Surjectivity and computing kernels


Kirwan proved that the restriction map from the equivariant cohomology of a Hamiltonian G-space to the ordinary cohomology of its symplectic reduction is a surjection.  Jeffrey-Kirwan and Tolman-Weitsman have provided methods for computing the kernel.  In this series of projects, I exploit these ideas to understand the topology of several different quotients.
I am currently working on three projects in this area.  With Reyer Sjamaar, I am working to understand the real loci of symplectic reductions by non-abelian groups.  With Rebecca Goldin and Allen Knutson, I am currently continuing the project on orbifold cohomology.  Finally, with Frank Sottile, I am trying to understand better the ideals that show up as kernels for symplectic reductions of flag varieties.