Andrea Tobia Ricolfi, Stavanger: Local contributions to Donaldson-Thomas invariants
Abstract: Donaldson-Thomas invariants are integers counting stable sheaves on Calabi-Yau 3-folds Y. In the rank 1 case, they can be interpreted as counting holomorphic curves on Y in a fixed homology class. We will define the "contribution" of a single smooth curve on Y to the full DT invariant of its homology class. We show how to compute these contributions and exhibit an explicit wall-crossing formula relating these local DT invariants to the local stable pair invariants, defined and computed by Pandharipande-Thomas.