Abstract:Much of the data of an algebraic variety is encoded by its (derived) category of vector bundles, and I will explain how it is sometimes possible to 'present' this category as the (derived) category of representations of a quiver. In such a situation, it is natural to consider the moduli space of stable representations of the quiver, which depends sensitively on your notion of stability. I will discuss the relationship between this moduli space and the original variety.