Stability conditions on Fukaya categories of surfaces: Some new techniques and results

          @misc{ scivideos_PIRSA:18080055,
            doi = {10.48660/18080055},
            url = {https://pirsa.org/18080055},
            author = {},
            keywords = {Mathematical physics},
            language = {en},
            title = {Stability conditions on Fukaya categories of surfaces: Some new techniques and results},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2018},
            month = {aug},
            note = {PIRSA:18080055 see, \url{https://scivideos.org/index.php/pirsa/18080055}}
          }
          

Abstract

In this talk I will present some upcoming 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. This definition is exclusive to the setting of these categories, and I will discuss problems and possibilities regarding generalization to other types of categories.