Chloé Postel-Vinay
University of Chicago
Title
k-shuffle polynomials
Abstract
One of the ways that braid groups manifest themselves is as fundamental groups of spaces of monic, complex, degree n polynomials with distinct roots. Another way to phrase this is: polynomials for which 0 is a regular value. In this talk, instead on focusing on just 0 being regular, we study spaces of polynomial for which the k roots of unity are regular values. Their fundamental groups are called k-shuffle braid groups (for which we will give a presentation), and these spaces also turn out to be classifying spaces. Finally, if time permits, we will see how k-shuffle braid groups inject into larger braid groups through polynomial homotopies.
