This workshop aims to bring together experts in the field to share their recent results on cutting-edge topics. Key topics include homological stability for Hurwitz spaces and the stacky perspective on counting problems. The workshop will also cover motivic approaches to counting and the new challenges of generalizing classical results to the wild case. We encourage participants to discuss ways to unify these ideas for further development.

Keywords: Hurwitz spaces (Homological stability), Malle's conjecture (for function fields), Rational points of stacks, Brauer-Manin obstruction (for stacks), Wild Galois extensions of function fields and power series fields (counting results, moduli spaces), Motivic counting of Galois extensions.

This event is part of the special year "Arithmetic, Homotopy, and Geometry 2027-28".