Noncrossing partitions, braid groups, and complex polynomials
Michael Dougherty, Lafayette
Abstract: The n-strand braid group is one of the most important objects in geometric group theory, in part because it lies in the overlap of many different classes of groups, including Artin groups and mapping class groups. Topologically, this group can be viewed as the fundamental group for the space of monic complex polynomials with distinct roots, and algebraically it is often defined using a generating set of n-1 diagrams depicting half-twists of adjacent strands. Work of Birman-Ko-Lee, T. Brady, and Bessis around the turn of the century introduced a new generating set for these groups which used the lattice of noncrossing partitions, and the combinatorics of this lattice has led to breakthroughs in our understanding of braid groups and Artin groups more generally. In this talk, I will describe some new connections between noncrossing partitions, braid groups, and complex polynomials. This is joint work with Jon McCammond.
Tea and refreshments available from 3:00-3:25 p.m. in the Assmus Conference Room (CU 212).
