Stability conditions in Fukaya categories: old and new ideas
Appears in collection : Mathematics Inspired by Physics
For the Fukaya category associated to a symplectic manifold with vanishing $c_1$, it is expected that closed complex-valued differential forms of middle degree subject to an open constraint each give rise to a Bridgeland stability structure (often called a stability condition in the literature). I will discuss related questions in differential geometry and attempts to formulate precise conjectures. The talk is based on earlier ideas developed together with Yan Soibelman, and on a current joint project with Fabian Haiden, Ludmil Katzarkov and Pranav Pandit.
