##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Brandon Alberts

#### UC San Diego

## Modeling Malle's Conjecture with Random Groups

##### Abstract:

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.

Host: Kiran Kedlaya

### October 29, 2020

### 2:00 PM

### See https://www.math.ucsd.edu/\~{}nts/

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