An operadic approach to the homology of Hurwitz spaces
Moduli and Friends seminar
Tuesday 7 February 2023
Craig Westerland (University of Minnesota) — An operadic approach to the homology of Hurwitz spaces
Hurwitz spaces of branched covers of A1 may be regarded as finite sheeted covers of configuration spaces of points in the line. Computing the (co)homology of these spaces is quite difficult. However, we may describe these homology groups as free algebras over a certain braided operad, and our goal becomes the computation of that operad. I'll present some partial progress in this computation, and an interpretation of the results in terms of the structure theory of braided Hopf algebras. Time permitting, we will investigate the action of the absolute Galois group on this system.
* Eastern European Time, i.e. UTC+2 in winter and UTC+3 in summer.