Automorphisms of positive entropy on some hyper-Kahler manifolds via derived automorphisms of K3 surfaces

Recently, Amerik and Verbitsky proved the existence of hyperKahler manifolds of Picard number two with automorphisms of positive entropy for a given deformation type of hyperKahler manifolds with the second betti number grater than four. However, explicit constructions of such hyperKahler manifolds are not known. In this talk, I would like to construct examples of automorphisms of positive entropy on hyperKahler manifolds of Picard number two as moduli spaces of stable objects in derived categories of K3 surfaces of Picard number one. Then the automorphisms are induced by autoequivalences of positive entropy on derived categories of K3 surfaces.