Quot schemes and their d-critical structure(s)

D-critical schemes and Artin stacks were introduced by Joyce in 2015, and play a central role in Donaldson-Thomas theory. They typically occur as truncations of (-1)-shifted symplectic derived schemes, but the problem of constructing the d-critical structure on a “DT moduli space” without passing through derived geometry (which is hard) is wide open. We discuss this problem, and new results in this direction, when the moduli space is the Quot scheme of points on a Calabi-Yau 3-fold. Joint work with Michail Savvas.