David Rydh: Canonical reduction of stabilizers for stacks with good moduli spaces

Some natural moduli problems give rise to stacks with infinite stabilizers. I will report on recent work with Dan Edidin where we give a canonical sequence of saturated blow-ups that makes the stabilizers finite. This generalizes earlier work in GIT by Kirwan and Reichstein, and on toric stacks by Edidin–More. Time permitting, I will also mention a recent application to
generalized Donaldson–Thomas invariants by Kiem–Li–Savvas.