Topology Seminar: Craig Westerland

I will explain some new techniques for computing the homology of braid groups with coefficients in a certain class of exponential representations that arise in a natural way from braided monoidal categories. Surprisingly (at least to me), these techniques are related to fundamental objects — Nichols algebras — in the theory of quantum groups and the classification theory of Hopf algebras. These techniques can be used to establish part of a function field analogue of Malle’s conjecture on the distribution of Galois groups. I will not discuss this application much in the topology seminar, but will focus on it in the colloquium. This is joint work with Jordan Ellenberg and TriThang Tran.