Symplectic resolutions arise in representation theory (Springer resolution), geometry (Hilbert–Chow morphism), and mathematical physics (3D mirror symmetry). There is a program to classify all symplectic resolutions of a given singularity. This classification simplifies, e.g., for certain Nakajima quiver varieties, when all such projective symplectic resolutions are given by variation of stability parameter [see Bellamy–Craw–Schedler].
Yet proper symplectic resolutions appear to be much more plentiful following Hubbard’s recent work in the hyperpolygon case, and Arbo–Proudfoot in the toric hyperkähler case. In joint work with Schedler, we construct new proper, non-projective symplectic resolutions for a large class of quiver varieties. The key idea is to build invariant Zariski-open subsets of representations of quivers generalizing subsets of semistable representations. In this talk, I will explain these ideas in a small example: a quiver variety with quiver affine D_4.
Note: there will be a lunch break at around noon, and the talk and/or discussions will continue over lunch in the lecture hall.