### 24/04/2019, 14:30 — 15:30 — Room P4.35, Mathematics Building

João Fontinha, *ETH Zurich*

### A primer on the Section Conjecture — a bridge between arithmetic and homotopy

In 1983, Grothendieck wrote a letter to Faltings in which he formulated a conjecture for hyperbolic curves over fields which are finitely generated over the rationals. Remaining open to date, it carries the study of rational points on an algebraic variety to the realm of profinite groups. Assuming only a working knowledge of basic Algebraic Geometry, we formulate and motivate the Section Conjecture and outline some modern attempts to tackle it.