Daniel Huybrechts (U Bonn):
Geometry of K3 surfaces and hyperkähler manifolds: Open problems and new perspectives
K3 surfaces and their higher-dimensional versions are geometric objects for which almost every
open conjecture in algebraic geometry has a specific meaning, a particularly beautiful answer or a sometimes
unexpected significance for the general situation.
In this talk we will discuss why K3 surfaces have their place next to Riemann surfaces, elliptic curves,
and abelian varieties, what it means to study their geometry and how linear algebra remains a most
efficient tool to phrase and answer questions. More abstract concepts like motives and categories, which
often shed a new light on purely geometric phenomena, will also make an appearance.