##### Department of Mathematics,

University of California San Diego

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### RTG Colloquium

## Ila Varma

#### UCSD

## Number field asymptotics and Malle's Conjecture

##### Abstract:

Malle's conjecture can be thought of as a generalization of the inverse Galois problem, which asks for every finite group $G$, is there a number field $K$ such that their Galois group over $\mathbb{Q}$ is isomorphic to $G$? Although open, this question is widely believed to be true, and Malle went further to predict the asymptotics of how many number fields there are with a given Galois group that only depended on the group structure of $G$ and the degree of the number field. In this talk, we will discuss the history as well as recent results and techniques surrounding these conjectures.

### May 31, 2019

### 2:30 PM

### AP&M 6402

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