K3 surfaces versus cubics

Algebraic geometry starts with cubic polynomials and the hypersurfaces they define form one of the most important classes of algebraic varieties (including elliptic curves and the famous cubic surfaces). Another and a priori totally unrelated class of geometric objects is provided by K3 surfaces. However, it has turned out by work of Hassett, Kuznetsov and many others that these two geometries are mysteriously linked. This talk will explain what we know about the relation and how it brings together transcendental and algebraic aspects.