The K(pi, 1) conjecture for affine Artin groups

Artin groups are a generalization of braid groups, and arise as the fundamental groups of configuration spaces associated with Coxeter groups. A long-standing open problem, called the K(pi, 1) conjecture, states that the higher homotopy groups of these configuration spaces are trivial. For finite Coxeter groups, this was proved by Deligne in 1972. In this talk I will present a recent proof of the K(pi, 1) conjecture in the affine case, which is a joint work with Mario Salvetti. The first part of the talk will be dedicated to introducing Coxeter groups, Artin groups, and the K(pi, 1) conjecture, so that only few topological and combinatorial prerequisites are needed.