K3 categories, cubic 4-folds, and Beauville-Voisin conjecture

We discuss recent progress on the connection between 0-cycles of holomorphic symplectic varieties
and structures of K3 categories. We propose that there exists a sheaf/cycle correspondence for any K3 category,
which controls the geometry of algebraic coisotropic subvarieties of certain holomorphic symplectic varieties. Two concrete cases will be illustrated in details: (1) the derived category of a K3 surface, (2) Kuznetsov category of a cubic 4-fold.