Inverse Galois Problem - Tim Dokchitser
Channel: IAS | Park City Mathematics Institute | PCMI
Date: 26/07/2021

2021 Graduate Summer School

Topic: Inverse Galois Problem
Speaker: Tim Dokchitser
Affiliation: Unversity of Bristol
Date: July 26, 2021

The Inverse Galois Problem asks whether every finite group occurs as a Galois group over Q. This question and its variant over Q(t) have driven a lot of research, and they are very interesting from a computational perspective as well. There are a variety of methods of constructing Galois groups, and they draw techniques from algebraic geometry, p-adic numbers, the theory of finite groups, Kummer theory, braid groups, group cohomology, and elliptic and modular curves, to name a few. In these lectures I will try to give an overview of the area, and explain where we stand. We will see how the various methods actually work for specific small groups, and get a feel for how far they can be pushed and what are the obstacles to solve the problem in general.

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