Speaker: Franc Forstneric (University of Ljubljana)

Title of the talk: What is an Oka manifold?

Abstract: Two classical theorems in the theory of holomorphic functions of one complex variable are the Runge approximation theorem and the Weierstrass interpolation theorem. I will discuss what happens when we try to generalize these results to holomorphic maps between complex manifolds. What transpires is that Stein manifolds are the natural sources of holomorphic maps, while Oka manifolds are the natural targets. I will describe how this subject developed over the last half century from the classical theories of Cartan and Oka-Grauert through the work of Gromov to its current state.