Donaldson-Thomas invariants are numerical invariants associated to Calabi-Yau varieties. They can be obtained by glueing singularity invariants from local models of a suitable moduli space endowed with a (-1)-shifted symplectic structure. By studying the moduli of such local models, we will explain how to recover Brav-Bussi-Dupont-Joyce-Szendroi's perverse sheaf categorifying the DT-invariants, as well as a strategy for glueing more evolved singularity invariants, such as matrix factorizations. This is joint work with M. Robalo and J. Holstein.