- Recorded June 2020: Hodge theory and the topology of hyper-Kähler manifolds: an introduction
- 06/03/2020: Polarized variations of Hodge structures of hyper-Kähler type
Recorded June 2020
TITLE: Hodge theory and the topology of hyper-Kähler manifolds: an introduction
ABSTRACT: After a short discussion of hyper-Kähler manifolds in the Riemannian and complex geometry contexts,
I discuss the general topological properties of hyper-Kähler
manifolds obtained from the local study of the period map. At the end of the talk, I start discussing
hyper-Kähler manifolds in the algebraic geometry setting, which will be the subject of the second lecture.
The audience for this lecture is encouraged to download the slides and to follow
along in the slides while watching the video.
June 3, 2020
TITLE: Polarized variations of Hodge structures of hyper-Kähler type
ABSTRACT: Like for abelian varieties and complex tori, the theory of projective hyper-Kähler manifolds is very different from the theory of general Kähler ones. The former is related via the period map and Torelli theorem to the study of certain quotients of bounded Hermitian symmetric domains by arithmetic groups. I will discuss various results concerning these moduli spaces and constructions of hyper-Kähler manifolds via algebraic geometry.