On Hypergeometric Motives and the Generalised Fermat Equation

In order to study the Generalised Fermat Equation $Ax^p + By^q = Cz^r$, Darmon defined what he called the Frey Representations. These local representations match, after specializing, the reduction coming from a geometric object. Therefore, they have the same ramification which will be crucial in the modularity method. However, instead of study explicitly these geometric objects, one can construct global representations coming from Hypergeometric Motives. The main purpose of this talk is to present an introduction to both, Generalised Fermat Equation and Hypergeometric Geometric Motives, and see how the latter present some advantages to study the former.