| Résume | A conjecture of Malle gives a prediction for the asymptotic growth of the number of number fields with a given Galois group when ordered by their discriminants. Recently, significant progress has been made on the function field analogue of this problem by leveraging topological and algebro-geometric techniques—specifically the homological stability of Hurwitz spaces. In this talk, I will explore the connection between Malle’s Conjecture and the topology of these Hurwitz space. I will then present my recent work, which utilizes these homological stability results to prove a version of Malle's conjecture over function fields with an explicit leading constant. |
