Modular Curves and Asymptotic Solutions to Fermat-type Equations

Abstract: Understanding solutions of Diophantine equations over a number field is one of the main problems of number theory. By the help of the modular techniques used in the proof of Fermat’s last theorem by Wiles and its generalizations, it is possible to solve other Diophantine equations too. Understanding quadratic points on the classical modular curve also plays a role in this approach. It is also possible to study the solutions of Fermat type equations over number fields asymptotically. In this talk, I will mention some recent results about these notions for the classical Fermat equation as well as some other Diophantine equations.

Mathematics

Audience: researchers in the topic

Greek Algebra & Number Theory Seminar