Stability Conditions, Quivers and Quadratic Differentials

In this talk I will introduce a potpourri of notions as a preparation for my research talk next week. Here I will review the concept of stability conditions on abelian and triangulated categories, using as a toy example categories arising from representations of quivers with potential. Those categories do carry a surprisingly rich structure and the associated spaces of stability conditions relate to moduli spaces of quadratic differentials on complex algebraic curves. The contents of this talk are intended as motivational background, but not as necessary material to appreciate the forthcoming research talk.