Modeling Malle's Conjecture with Random Groups

Abstract: We construct a random group with a local structure that models the behavior of the absolute Galois group ${\rm Gal}(\overline{K}/K)$, and prove that this random group satisfies Malle's conjecture for counting number fields ordered by discriminant with probability 1. This work is motivated by the use of random groups to model class group statistics in families of number fields (and generalizations). We take care to address the known counter-examples to Malle's conjecture and how these may be incorporated into the random group.

number theory

Audience: researchers in the topic

Comments: pre-talk at 1:30

UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.