Gaberdiel, Hohenegger and Volpato (GHV) characterized automorphism groups of K3 sigma models in terms of Mukai lattice and Leech lattice. Huybrechts gave a geometric interpretation of GHV Theorem in terms of derived categories of K3 surfaces and Bridgeland stability conditions on them. As a result, autoequivalence groups of derived categories of K3 surfaces are related with certain subgroups of the Conway group. On the other hand, Laza and Zheng classified automorphism groups of cubic fourfolds. In particular, symplectic automorphism groups of cubic fourfolds are characterized as certain subgroups of the Conway group.
In this talk, I would like to study the direct relations between automorphism groups of cubic fourfolds and autoequivalence groups of K3 surfaces.