Speaker
Description
Thomas, Yau and Joyce made the remarkable conjecture that the existence of a special Lagrangian submanifold representing a fixed Fukaya equivalence class on a Calabi-Yau manifold should be equivalent to the stability of that class with respect to a suitable Bridgeland stability condition on the Fukaya category.
I will describe work in progress towards proving the implication from Bridgeland stability to the existence of a special Lagrangian for some nontrivial examples, namely certain Lagrangian spheres in suitable K3 surfaces or products of such K3 surfaces with an elliptic curve.
The proposed approach uses mirror symmetry for K3 surfaces rather than more standard but difficult analytic methods such as the Lagrangian mean curvature flow or gluing, but I will discuss why it should be (conjecturally) equivalent to a gluing construction.