In this talk I will explain a general mechanism, based on derived symplectic geometry, to glue the local invariants of singularities that appear naturally in Donaldson-Thomas theory. Our mechanism recovers the categorified vanishing cycles sheaves constructed by Brav-Bussi-Dupont-Joyce, and provides a new more evolved gluing of Orlov’s categories of matrix factorisations, answering a conjecture of Kontsevich-Soibelman and Y. Toda. This is a joint work with B. Hennion (Orsay) and J. Holstein (Hamburg). The talk will be accessible to a general audience.