Yoosik Kim, Disk Counting via GIT Quotients

According to the Kempf–Ness theorem, the GIT quotient is equivalent to the symplectic reduction. Using this correspondence, we explain how to relate the counting of holomorphic disks between a symplectic manifold equipped with a Hamiltonian group action and its symplectic reduction. As an application, we derive the disk potential function for weight varieties obtained as quotients by the maximal torus of partial flag varieties. We also demonstrate how the disk counting depends on the choice of stability conditions.