Ivan Marin: Braid groups associated to complex reflection groups
In 1998, in view of defining generalized Hecke algebras associated to an arbitrary complex reflection group, Broué, Malle and Rouquier investigated generalized braid groups, which provide a further generalization of Artin groups of finite Coxeter type. They stated a number of theorems and conjectures, which are all proved now. In this talk I will recall this background material, and describe some of the tools involved in the proofs. In particular, the determination of the center of the generalized pure braid groups made use of special monoids associated to these groups, whose (Garside) properties are similar to the properties of more classical Artin monoids.
