Tudor Pădurariu
Columbia University, New York, USA

Donaldson-Thomas invariants (DT) are (integer) virtual count of sheaves on a threefold. For Calabi-Yau threefold, there are several refinements of DT invariants, for example to a graded vector space whose Euler characteristic is the numerical DT invariant. When the threefold is a local surface, there are further refinements to a dg category, due to Yukinobu Toda. I will explain joint results with Yukinobu Toda on the structure of these categorifications of DT invariants. I will focus on the example of points on $\mathbb{C}^3$. I will also discuss the construction of a categorical analogue of BPS invariants of $\mathbb{C}^3$ and their application in a categorical DT/ Pandharipande-Thomas (PT) correspondence.