Galois sections and p-adic period maps (live stream)

In a by now famous letter to Faltings, Grothendieck predicted that for hyperbolic curves over number fields the set of rational points has a description in terms of Galois theory of its étale fundamental group. We will explain what the recent p-adic proof of the Faltings-Mordell theorem due to Lawrence and Venkatesh can teach us about Grothendieck's Section Conjecture. (joint work with L. Alexander Betts)