k-shuffle braid groups (Math Colloquium Series)

Abstract: In this talk, we introduce a new family of groups called the k-shuffle braid groups. We will see how they arise in two different contexts: an apparently very combinatorial one, as the fundamental group of a CW-complex obtained from the poset of k-shuffle non-crossing partitions, and a more geometric context as the fundamental group of spaces of complex monic polynomials with a certain set of prescribed regular values. We will see that both spaces are classifying spaces, and if time permits, how to go from one to the other.