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.