On quivers and exceptional collections for projective toric manifolds.
I will describe how certain collections of line bundles on a projective toric manifold can be used to construct the manifold as a moduli space of quiver representations. Put another way, I will introduce new quiver gauge theory constructions of these manifolds. The condition on the line bundles is quite weak, and in particular it holds for a complete strong exceptional collection (if one exists). This programme leads to new examples of such collections. This is joint work with Gregory Smith.