Extremal rays and automorphisms of holomorphic symplectic varieties

We survey recent results on ample cones and birational contractions of holomorphic symplectic varieties of K3 type, focusing on explicit constructions and concrete examples.Comment: 24 page

Rational points on K3 surfaces and derived equivalence

We study K3 surfaces over non-closed fields and relate the notion of derived equivalence to arithmetic problems.Comment: 30 page