# Seminar of Algebra

### The inverse Galois problem, Jacobians and the Goldbach's conjecture

Speaker:
Samuele Anni (Max Plank Institute for Mathematics)
Email:
samuele.anni@gmail.com
Location:
Departamento de Álgebra
Date:
Tue, 12 dec 2017 12:30
Anni Samuele is a postdoctoral researcher at the Max Plank Institute for Mathematics in Bonn. The main topics of his research are the study of Galois representations and automorphic forms.

The inverse Galois problem is one of the greatest open problems in group theory and also one of the easiest to state: is every finite group a Galois group?

My interest around this problem is connected to the realization of linear and symplectic groups as Galois groups over $\mathbb{Q}$ and over number fields. In particular, I am interested in "uniform realizations": realizations of all elements in a family of groups (e.g. $GL_2(\mathbb{F}_\ell)$ for every prime $\ell$) simultaneously using only one "object". In this talk I will describe uniform realizations using elliptic curves, genus 2 and 3 curves.

After this introduction, I will explain how to extend these results via Jacobians of higher genus curves. This is joint work with Vladimir