IHS Manifolds: Automorphisms, Kahler cones and related questions

After a (dramatically brief) introduction on IHS or Hyperkähler manifolds, we will survey several results on the shape of their Kähler cones and related cones in the projective setting (ample, movable) and a Boucksom-Zarisky decomposition for divisors. Then, we sketch how these properties can be used to describe automorphisms of IHS manifolds.