# Seminário de Teoria Quântica do Campo Topológica

### The Fermat equation over totally real number fields

Jarvis and Meekin have shown that the classical Fermat equation $x^p + y^p = z^p$ has no non-trivial solutions over $\mathbb{Q}(\sqrt{2})$. This is the only result available over number fields. Two major obstacles to attack the equation over other number fields are the modularity of the Frey curves and the existence of newforms in the spaces obtained after level lowering.

In this talk, we will describe how we deal with these obstacles, using recent modularity lifting theorems and level lowering. In particular, we will solve the equation for infinitely many real quadratic fields.

Organizadores correntes: Roger Picken, Marko Stošić.

Projecto FCT PTDC/MAT-GEO/3319/2014, Quantization and Kähler Geometry.