Number Theory Seminar

For $G$ a finite group, Malle's conjecture predicts the asymptotic growth of the number of $G$ extensions of a fixed global field. In joint work with Ishan Levy, we compute the asymptotic growth of the number of Galois $G$ extensions of $\mathbb F_q(t)$, for $q$ sufficiently large and relatively prime to $|G|$. Time permitting, we may also mention an extension of these methods toward verifying the Poonen-Rains conjectures about average sizes of Selmer groups of elliptic curves in quadratic twist families.