Fundamental group is one of the first algebraic invariants one learns in algebraic topology. Beyond the definition, one learns how to associate the fundamental group with covering spaces. The issue with this approach in algebraic geometry is the lack of a universal cover (due to our requirement for finite type schemes). We use an analogue of covering spaces, namely finite etale maps, to define the Etale fundamental group. Yet another issue with this, is the requirement that the base point be in a separable extension rather than the field itself (i.e the difference between a rational point and a point in a field extension). We resolve that by introducing the Nori fundamental group. In this talk I'll give examples of all 3 kinds of "fun"damental groups.
Zoom Link: https://washington.zoom.us/j/92849568892