# The $K(\pi,1)$ conjecture for affine Artin groups – Giovanni Paolini (Caltech, USA)

#### Abstract

​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 the first part of this talk, I will introduce Coxeter groups, Artin groups, and the $K(\pi,1)$ conjecture (so that only a few topological and combinatorial prerequisites are needed). Then I will outline a recent proof of the $K(\pi,1)$ conjecture in the affine case, which is joint work with Mario Salvetti.

Click here for the slides of the talk and here to see the video of the talk.

Further information is available on the event page on the Indico platform.

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