Refining Malle's Conjecture for Inductive Counting Methods

Abstract: Malle's conjecture predicts the asymptotic growth rate of the number of G-extensions F/K of a number field K with absolute discriminant bounded above by X, where X tends towards infinity. I will discuss a joint project with Robert Lemke Oliver, Jiuya Wang, and Melanie Matchett Wood to approach this conjecture inductively by first restricting to G-extensions F/K containing a fixed intermediate extension L/K, then taking a sum over choices of intermediate extensions. A fundamental concept in this talk will be the related question of finding the distribution of elements of the first Galois cohomology group, $H^1(K,T)$. In particular, I will address a joint paper with Evan O'Dorney using harmonic analysis to study $H^1(K,T)$.

number theory

Audience: researchers in the topic

UCLA Number Theory Seminar