Starting with a sufficiently nice Artin stack, we explain a canonical blowup procedure that produces a Deligne-Mumford stack, resolving the locus of points with infinite automorphism group. This construction can be applied to moduli stacks parametrizing semistable sheaves or complexes on Calabi-Yau threefolds. We show that their stabilizer reductions admit natural virtual fundamental cycles, allowing us to define generalized Donaldson-Thomas invariants which act as counts of these objects. Everything in this talk is expected to be the shadow of a corresponding phenomenon in derived algebraic geometry, giving a new, derived perspective on Donaldson-Thomas invariants.

Based on joint work with Young-Hoon Kiem and Jun Li and joint work in progress with Jeroen Hekking and David Rydh.