Craig Westerland, University of Minnesota

Abstract: Hurwitz moduli spaces parameterize branched covers of algebraic curves.  In this talk, I’ll focus on branched covers of the affine line and explain several approaches to understanding the cohomology of these moduli spaces using connections to braided Hopf algebras and a new family of braided operads.  In particular, I hope to convey how an operad which governs multiplicative operations on Hurwitz spaces also controls primitives in braided Hopf algebras.  Time permitting, I’ll also discuss what little can be said about the action of the absolute Galois group on these cohomology rings.