CORDIS Project
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This project tackles the Generalized Fermat Conjecture in number theory by developing a strategy to apply the modular method to generalized Fermat equations. It aims to establish modularity results for hypergeometric motives and prove new instances of the conjecture involving distinct prime exponents.
This project addresses the Generalized Fermat Conjecture, one of the most challenging open problems in number theory.
While the modular method has led to remarkable breakthroughs, including the proof of Fermat’s Last Theorem, its application to more general equations remains limited.
Recently, a new framework was introduced by the supervisor through the use of hypergeometric motives, opening an unexplored direction for research.
At the same time, the ER has contributed to Darmon’s program, a com…
UNIVERSIDADE DE AVEIRO
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