# Manchester Number Theory Seminar - Philippe Michaud-Jacobs

Dates: | 9 May 2023 |
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Times: | 15:00 - 16:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Current University students |

Speaker: Philippe Michaud-Jacobs (Warwick)

Title: Isogenies of elliptic curves and Diophantine equations

Abstract: Isogenies are the basic building blocks of maps between elliptic curves. In 1978, Mazur gave a complete classification of the possible prime degrees of isogenies between elliptic curves defined over the rationals. This result is now known as Mazur's isogeny theorem, and perhaps its most spectacular consequence is the pivotal role it plays in the proof of Fermat's Last Theorem. In this talk, I will discuss Mazur's isogeny theorem, some ideas behind its proof, and the way it features in the resolution of various families of Diophantine equations within the framework of a strategy known as the modular method. I'll also focus on the challenges one faces when seeking to extend Mazur's isogeny theorem to number fields other than the rationals, state some results obtained in this direction, and highlight some important Diophantine consequences.

Room: Frank Adams 1