| A vector bundle E on a variety X embedded in a n-dimensional projective space is Ulrich if for some linear projections X in P^{n-1} the direct image of E is trivial. The existence of an Ulrich bundle on a k-dimensional variety X implies that the cone of cohomology tables is the same as for the k-dimensional projective space. It is expected that every projective variety admits an Ulrich bundle. We will discuss how Lazarsfeld-Mukai bundles on K3 surfaces provide examples of rank 2 stable Ulrich bundles. Our results imply, by using the work of Eisenbud and Schreyer, that the Chow form of a polarized K3 surface admits a pfaffian Bézout form in Plücker coordinates. This is a joint work with Gavril Farkas and Marian Aprodu. |