Abstract: After a brief review of classical function theory on $\mathbb C$, we will discuss its extension to functions with values in an algebraic variety, i.e. an entire holomorphic curve, and motivate the fact that such a curve should be constrained by birational invariants of the variety that pertains to "hyperbolicity." We will verity this conjectural fact for varieties of maximal Albanese dimension, itself a birational invariant. We will assume no prior knowledge of birational geometry. This is joint work with Joerg Winkelmann.

Abstract: I will introduce the basic concepts and results in coding theory and I will explain how these can help determine the maximum number of collinear points from a finite set of points in the plane given by their coordinates.