Constructing stability conditions on Fukaya categories by using relative versions of stability conditions 

In this talk I will present some recent work on Bridgeland stability conditions on partially wrapped Fukaya categories of topological surfaces. The main result is a proof that the stability conditions defined by Haiden, Katzarkov and Kontsevich using quadratic differentials cover the entire stability space. This proof uses a definition of the new concept of relative stability conditions, which is a relative version of Bridgeland's definition, with functorial behavior analogous to compactly supported cohomology. Time allowing I will also discuss possible generalizations of this concept to other categories, and possible relations to the study of dynamics on surfaces.