Emil Jacobsen: On motivic fundamental groups

Abstract

I will introduce the (generic) motivic fundamental group, by analogy with the étale fundamental group. Then, I will explain the relationship between this group and the topological fundamental group, as well as what this relationship says about motivic local systems. Along the way, I will cover analogous results in Hodge theory. At the end, I will talk about the group theoretic theorem which underpins these results, and say a few words about its proof. If there's time, I might mention some applications to de Rham fundamental groups.