2015, Max Planck Institute for Mathematics
von Känel, Rafael; Matschke, Benjamin
We discuss certain classical Diophantine equations and we explain how geometry can help to understand their solutions. In particular we consider some highlights in the field of Diophantine equations, including Faltings' resolution of the Mordell conjecture and Wiles' proof of Fermat's last theorem. We also discuss a project at the MPIM Bonn which combines the methods of Faltings and Taylor-Wiles in order to make some progress concerning the classical problem of finding all squares and cubes of given difference.