Non displaceable Lagrangian submanifolds

Non-displaceability of certain Lagrangian submanfolds is a rigidity phenomenon in symplectic geometry. There are well-known sufficient conditions for non-displaceability. One is non-vanishing of Lagrangian intersection Floer cohomology. The other is (super)heaviness due to Entov and Polterovich. (Note that the latter is defined for any subsets, which are not necessarily Lagrangian submanifolds.) I will explain the relation between these conditions and present some examples based on joint work with Fukaya, Oh and Ohta. If time allows, I will discuss another argument for superheaviness of certain subsets.