Density of integral points over function fields -- Brendan Hassett

(joint with Tschinkel) Consider a pair consisting of a smooth projective variety and a normal-crossings divisor, defined over the function field of a complex curve B. For a model (X,D) over B, integral points are sections B--->X meeting D only over prescribed points of B. We summarize density results for integral points on log Fano pairs, as well as some open problems.