Nikolas Kuhn (University of Oxford)

The Joyce-Song wall-crossing formulas for Donaldson-Thomas invariants of Calabi-Yau threefolds have proven to be a crucial and versatile tool. In the presence of a torus action, there are interesting threefold geometries in which the Calabi-Yau condition only holds up to an equivariant twist – examples include Vafa-Witten invariants, local curves and surfaces and the threefold vertex. In these cases, invariants are defined using localization, and Joyce-Song’s theory doesn’t apply. I will explain how ideas from Joyce’s recent work on wall-crossing in abelian categories can be used to prove wall-crossing in this situation, and which difficulties arise.  This is joint work with Henry Liu and Felix Thimm.