Welcome!

The geometry of K3 surfaces is very rich; their higher-dimensional generalizations---known as hyperkähler manifolds---share much of the same richness.  The goal of this course is to survey the basic theory of hyperkähler manifolds.  Topics will include:  basic definitions and examples, Hodge theory and deformation theory, birational geometry, the global Torelli theorem, and algebraic moduli.  Time permitting we may also discuss some relations to more general Calabi--Yau manifolds.