Lucas Villagra Torcomian

In this talk we will briefly review the modular method, the strategy used by Wiles to prove Fermat’s Last Theorem. We will then explain how hyperelliptic curves have emerged as an important tool in recent years to approach generalized Fermat...

After a brief review of the modular method, in this talk we will explain how hyperelliptic curves have emerged as an important tool in recent years to approach generalized Fermat equations.

In this talk we will introduce the modular method, the approach followed by Wiles to prove Fermat’s Last Theorem. We will explain the role of elliptic curves, modular forms, and Galois representations in this framework, and discuss how the method has...

In 1770 Euler observed that 3 3 + 4 3 + 5 3 = 6 3 and asked if there was another perfect power that equals the sum of consecutive cubes. This captivated the attention of many important mathematicians, such as Cunningham, Catalan, Genocchi and Lucas...

Let f and g be two newforms with equal coefficient fields. In this talk we will see how a congruence between the Galois representations of f and g for a sufficiently large prime p implies strong conditions between the algebras of endomorphisms of the...

In 1770 Euler observed that $3^3+4^3+5^3=6^3$ and asked if there was another perfect power that equals the sum of consecutive cubes. This captivated the attention of many important mathematicians, such as Cunningham, Catalan, Genocchi and Lucas. In...