Title:
Finding examples of primary Burniat surfaces with many sporadic
rational points

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. Due
to results of Faltings, Kawamata, Chevalley and Weil the conjecture
holds for primary Burniat surfaces. In this talk, we will present
examples of primary Burniat surfaces with many sporadic rational points.