Seminar

Moduli spaces of meromorphic quadratic differentials can be viewed as spaces of stability conditions on certain triangulated categories defined either as Fukaya categories or via quivers with relations. This abstract point-of-view predicts the existence of further structure on these spaces, namely a bundle of tori equipped with a pencil of connections. In the case of quadratic differentials I will explain how this structure can be described explicitly in terms of isomonodromic families of opers. This is closely related to the paper of Gaiotto, Moore and Neitzke on wall-crossing and the Hitchin system.