Abstract：

To the singularities of a hypersurface one may associate increasingly sophisticated invariants: Milnor numbers, sheaves of vanishing cycles and categories of Matrix factorizations. It is an interesting problem to globalize these locally defined invariants. The Milnor numbers associated to the moduli spaces of suitable sheaves on a Calabi-Yau 3-fold leads to the highly influential Donaldson-Thomas invariants. Brav-Bussi-Dupont-Joyce-Szendroi have globalized the sheaf of vanishing cycles to construct a categorification of Donaldson-Thomas invariants (obstructed by some orientation data). I will take about globalizing higher categorical invariants. This depends on the study of (-1)-shifted symplectic structures on derived schemes, but I will not expect the audience to know what those words mean. This is work in progress, joint with B. Hennion and M. Robalo.