Title: Non-Archimedean analytic curves in algebraic varieties

Abstract: I will explain Serge Lang's conjectures relating four aspects of
algebraic varieties: geometric structure, rational maps from group
varieties, rational points, and holomorphic maps from the complex plane. I
will then explain what happens if one considers non-Archimedean analytic
maps instead of complex holomorphic maps and discuss a parallel conjectural
framework. I will give a broad overview and intend that the talk will be
accessible even to those with limited experience with algebraic geometry and
non-Archimedean analysis.