Samir Siksek
University of Warwick, UK

A Multi-Frey Approach to Diophantine Equations

At the heart of Wiles' proof of Fermat's
Last Theorem is a device called the 'Frey curve'. The
Frey curve is now typically used to derive information
about solutions to Diophantine equations. In this
talk, which is based on joint work with Bugeaud and
Mignotte, we explain a powerful refinement which uses
several Frey curves simultaneously. For example, we
solve the equation 2^r 3^s x^n- 5^t y^n=1.