Alex Takeda (UC Berkeley)

Sunday, November 25, 2018 - 1:30pm to 2:30pm

PDL C-36

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.