Many interesting examples of singular symplectic algebraic varieties and their symplectic resolutions are built by Hamiltonian reduction. There is a corresponding construction of "quantum Hamiltonian reduction" which is of substantial interest to representation theorists. It starts from a twisted-equivariant D-module, an analogue of an algebraic vector bundle (or coherent sheaf) on a moment map fiber, and produces an object on the quantum analogue of the symplectic resolution. In order to understand how far apart the quantisation of the singular symplectic variety and its symplectic resolution can be, one wants to know "what gets killed by quantum Hamiltonian reduction?" I will give a precise answer to this question in terms of effective combinatorics. The answer has consequences for exactness of direct images, and thus for t-structures, which I will also explain. The beautiful geometry behind the combinatorics is that of a stratification of a GIT-unstable locus called the "Kirwan-Ness stratification." The lecture will not assume familiarity with D-modules, nor with any previous talks by the speaker or McGerty in this series. The new results are joint work with McGerty.
