Lagrangian embeddings of cubic fourfolds containing a plane

I will talk about the construction of Lagrangian embeddings of cubic fourfolds containing a plane.
Recently, Lehn et al constructed Lagrangian embeddings of cubic fourfolds NOT containing a plane via twisted cubic curves on cubic fourfolds.
In this talk, we will construct desired holomorphic symplectic 8-folds as moduli spaces of Bridgeland stable objects in derived categories of some twisted K3 surfaces.