# Mathematics Colloquia and Seminars

Orientation data is an ingredient in the definition of Motivic Donaldson-Thomas(DT) invariant. Roughly speaking, it is a square root of the virtual canonical bundle on a moduli space. In this talk, I will briefly introduce Motivic DT invariant, and the role of orientation data in its definition. I will then give a construction of orientation data for the stack of coherent sheaves on local $$P^2$$ based on the canonical orientation data from quiver representations. I will also show that this orientation is the same as the one from geometry due to Maulik and Toda.