Mathematics

Donaldson-Thomas invariants are integers (virtually) counting sheaves on complex 3-folds. The local structure of the moduli space of sheaves on a Calabi-Yau 3-fold leaves room for various refinements of these integer counts. After introducing some of them, we will give an example (joint work with B. Davison) of a motivic refinement in DT theory: a motivic lift of the DT/PT correspondence, proved in the unrefined case by Bridgeland and Toda.