Abstract Victoria Hoskins

Victoria Hoskins will speak on

Stratifications for representations of quivers and sheaves

Abstract: Many moduli spaces are constructed via geometric invariant theory and in this talk we focus on moduli of coherent sheaves and moduli of quiver representations. In both cases, we introduce two stratifications: a Harder-Narasimhan stratification and a stratification coming from the GIT construction, which has a more combinatorial flavour. For quiver representations, we show that both stratifications coincide. However, this is not quite true for sheaves. We explain why this is the case and we instead construct an asymptotic GIT stratification which agrees with the Harder-Narasimhan stratification for sheaves. If there is time, we will also explain some applications to the construction of moduli spaces of unstable objects.