Nick Kuhn (UiO) - Spin structures on perfect complexes

I will explain how to extend the concept of spin structures from vector bundles to complexes over a scheme (or algebraic stack) X outside of characteristic 2. For a complex E on X with an oriented quadratic structure one obtains an associated Z/2Z-gerbe over X obstructing the existence of a spin structure on E. I will also touch on an expected alternative definition of spin structures on complexes using derived Clifford algebras. One application of the concepts presented is to give a refinement of the virtual structure sheaf of Oh-Thomas in Donaldson-Thomas theory of Calabi-Yau fourfolds.