The abelian/nonabelian correspondence in Gromov-Witten theory I

Given a "good" action of a reductive complex algebraic group G on a projective manifold X, the abelian/nonabelian correspondence refers to a precise relation that exists between topological invariants (cohomology, K-theory) of the Geometric Invariant Theory quotients X//G and X//T, where T is a maximal abelian subgroup in G. In this series of talks, we will explain how to extend this relation to the (genus zero) Gromov-Witten theories of the two quotients, based on joint works with Aaron Bertram and Claude Sabbah.