Rafael Andrist

The first part of the talk consists of an introduction to Andersen-Lempert
theory and the density property for Stein manifolds, which is a notion
expressing that a manifold has many holomorphic automorphisms. The most
important consequence of the density property is a Runge-type
approximation theorem for holomorphic automorphisms which has many
interesting geometric implications, in particular the automorphism group
acts multi-transitively.

The second part of the talk focusses on affine surfaces with the density
property. The goal is to find all affine surfaces with the density
property. Gizatullin described all affine surfaces with a quasi-transitive
group action, hence all candidates of affine surfaces with the density
property must be found in the class of these so-called Gizatullin
surfaces.
We describe a subclass of Gizatullin surfaces that indeed has the density
property.