Curves and cycles on K3 surfaces vs. A recent intrusion of algebraic geometry into stable homotopy theory

Huybrechts: Curves and cycles on K3 surfaces

This talk will survey some older and more recent results concerning the geometry of K3 surfaces. In particular, we will stress the role of special curves (rational and elliptic) for the study of the Chow group. Certain features of the Chow group of a K3 surface are rather well understood thanks to a result of Beauville and Voisin. Others, eg the behaviour of CH^2(X) for X over small fields or under base change rather poorly.

Levine: A recent intrusion of algebraic geometry into stable homotopy theory

With Voevodsky's introduction of motivic stable homotopy category, a new channel of communication been algebraic geometry and algebraic topology has been opened. I will present a few basic constructions in stable homotopy theory, such as the Postnikov tower and the Adams-Novikov spectral sequence, and how these have motivic analogs. I will also explain how the motivic versions turn around and relate to the purely topological constructions, opening the way to a new introduction of algebraic geometry and arithmetic in stable homotopy theory.