Construction of Galois extensions

Abstract: The inverse Galois problem asks whether every finite group can be realized as the Galois group of a finite extension of $\mathbb{Q}$. In this talk, we will discuss the cases of $S_n$ and $\text{PGL}_2(\mathbb{F}_p)$. These methods can also be adapted to apply to the simple groups $A_n$ and $\text{PSL}_2(\mathbb{F}_p)$ (for many $p$).

algebraic geometrynumber theory

Audience: advanced learners

STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Fall 2025 topic: Weil conjectures.

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.