Title:
The explicit Bombieri-Lang conjecture for generalized Burniat type surfaces

Abstract:
The Bombieri-Lang Conjecture states that most of the rational points on a smooth projective surface S of general type defined over the field of rational numbers lie on finitely many curves of geometric genus 0 or 1 contained in S. Furthermore, the set of rational points on S outside these curves is finite and we call these sporadic rational points. The conjecture holds for surfaces of general type admitting a finite étale covering such that the covering surface is contained in a product of abelian varieties and curves of higher genus. In this talk we look at how to make this result effective for some families of surfaces of general type, specifically generalized Burniat type surfaces.