Fox-Neuwirth/Fuks cells, quantum shuffle algebras and Malle’s conjecture for function fields

Seminar/Forum

 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.

Presenter

  • Dr TriThang  Tran
    Dr TriThang Tran, University of Melbourne