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Title: k-shuffle braid groups

Abstract: Braid groups are known to arise as from many places, two of which are as the Garside group obtained from the poset of non-crossing partitions, and as the fundamental group of the space of square-free complex polynomials of degree n. The latter is a K(B_n,1) while the former can be used to build a CW-complex with nice combinatorial properties, which is also a K(B_n,1). In 2024, McCammond and Dougherty described explicitly the homotopy allowing to go from one to the other.

In this talk, we introduce a new family of groups called the k-shuffle braid groups. We will see how they arise in two similar contexts: first, we will look at certain families of non-crossing partitions and obtaining a (metric) CW-complex following classical arguments from Garside theory for Artin groups. Second, from 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. Finally, we will briefly discuss the CAT(0) property for the CW-complex.

We will gather for teatime in the lounge at 4pm after the talk, and then we will go for dinner with Chloé.

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