Fox-Neuwirth/Fuks cells, quantum shuffle algebras and Malle’s conjecture for function fields
In 2002, Malle formulated a conjecture about the distribution of number fields with a specified Galois group.
The first part of this talk will serve as an introduction to Malle’s conjecture for function fields. I will then show how topology can be used to study Malle’s conjecture. Central to this discussion will be getting bounds on the (co)homology of Hurwitz spaces — moduli spaces for branched covers. Somewhat surprisingly, these computations can be tackled through the homological algebra of certain braided Hopf algebras arising in the classification of pointed Hopf algebras.
Dr TriThang Tran, University of Melbourne