Artin groups and non-positive curvature, I

Artin groups arise naturally in the study of braid groups, Coxeter groups and hyperplane arrangement. Despite the simplicity of their definition, many basic questions remain open. Many previous approaches for understanding Artin groups have a common feature - they relies on certain form of non-positive curvature (NPC) on such groups. This leads to the conjecture that all Artin groups are NPC in an appropriate sense. We take the viewpoint of geometric group theory, and explain various cases where it is possible to put NPC structure on Artin groups, some of these cases are classical and some are more recent. Part of the minicourse is based on joint work with D. Osajda.