Introduction to Artin groups and K(pi,1)-conjecture

Abstract：

A hyperplane arrangement in C^n is the manifold obtained by removing a collection of affine complex dimension one hyperplanes from C^n. Despite the simplicity of the definition and the long history of studying them, even basic questions on their fundamental groups still remain open. One important scenario of studying, is that the collection of hyperplanes has extra symmetry - namely there is a group acting on C^n permuting the hyperplanes. We will explain how this is related to the study of reflection groups, and braided versions of reflection groups - Artin groups. We will also discuss some background on one central conjecture in this direction, namely the K(pi,1)-conjecture for reflection arrangement complements.