GAAG seminar - The pseudo-effective cone of a hyper-Kähler manifold and polygons of Newton-Okounkov type

Hyper-Kähler (HK) manifolds form one of the three building blocks of compact Kähler manifolds with vanishing first (real) Chern class. In recent years, there has been a considerable effort by many mathematicians to understand as much as possible about the geometry of these varieties. Despite everything, the positivity of divisors is one of the least understood things in HK geometry. The purpose of this talk is to discuss some results about the positivity of divisors on HK manifolds, which, in some sense, generalise some results from the theory of smooth projective surfaces and provide further credibility to the heuristic that linear series on HK manifolds behave very much like in the surface case.