Joint IAS/Princeton University Symplectic Geometry Seminar

I will report on recent joint work with L. Katzarkov and M. Kontsevich (arXiv:1409.8611) in which we construct Bridgeland stability conditions on partially wrapped Fukaya categories of surfaces. Stable objects in these stability conditions correspond to finite-length geodesics (with local system) with respect to some flat metric with conical singularities given by a quadratic differential. The proof relies on the fact that all objects in the derived Fukaya category of a surface are geometric, i.e. come from immersed curves with local system. Examples and some further directions will also be discussed.