Fermat’s Last Theorem, in other words for the Diophantine equation
$$x^n + y^n = z^n,\quad n ≥ 3,$$
there do exist integers \(x, y, z \in \mathbb{Z}\) with \(xyz \neq 0\), it was an open problem that mathematicians studied hard for more than 350 years. One of the greatest achievements in Number Theory during the 20th century was its proof by Andrew Wiles in 1995.
Central role in Wiles’ proof was the connection between two different areas of mathematics, the “algebraic/geometric” world of elliptic curves and the “analytic” world of modular forms through the theory of Galois representations. This connection opened a completely new area in Diophantine equations, which will call the modular method nowdays.
In this seminar we will have an introduction in the theory of elliptic curves, modular forms and Galois representations. The main goal of the seminar is the understanding of the modular method and how it is used in the resolution of Diophantine equations.
The seminar is open to anyone how is curious to see modern methods in Diophantine equations. Our meetings are every Thursday 10:00-12:00, room M2, and the first meeting will take place on 15th February 2024 through Zoom.
Please register for the seminar here in order to get the Zoom link.
For more information you can contact Assistant Prof. Angelos Koutsianas (akoutsianas@math.auth.gr).