Speaker: Christopher Woodward (Rutgers University)

Title: Gauged Gromov Witten Theory and wall-crossing, III

Abstract: I will describe a quantum version of the Kirwan map, which is a non-linear map from QH_G(X) to QH(X // G) which is a homomorphism on each tangent space, and relates the graph Gromov-Witten invariants of X // G with the gauged Gromov-Witten invariants of X in the limit of large stability parameter. I will give some toric examples, and describe a correspondence using Venugopalan's thesis which relates the algebraic picture to the symplectic picture studied by Gaio, Salamon, and Ziltener. Combining this with the wall-crossing for gauged Gromov-Witten invariants one obtains the wall-crossing formula for Gromov-Witten invariants under variation of git quotient, and in particular, a proof of the crepant transformation conjecture in the git case. This is partly joint with Eduardo González and Sushmita Venugopalan.