Galois sections and p-adic local systems

One theoretical technique used in the study of rational points on a variety X is to attach to every rational point x a Galois representation V_x, and then use facts about these Galois representations to say something about x. This idea underpins both Faltings' original proof of the Mordell Conjecture, and the Chabauty—Kim method for computing rational points on curves. In this talk, I will explain how one can use similar ideas to study sections of Grothendieck's fundamental exact sequence, and touch on some applications in work with Jakob Stix, Martin Lüdtke and Theresa Kumpitsch.