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SUMMARY:On the Darmon program for the Generalized Fermat equation [MPIM]
DTSTART:20250213T140000Z
DTEND:20250213T150000Z
DTSTAMP:20260420T154900Z
UID:indico-event-246@math-events.uni-bonn.de
DESCRIPTION:Speakers: Nuno Freitas (MPIM)\n\nMPI-Oberseminar\nIn 2000\, Da
 rmon described a remarkable program to study the Generalized Fermat equati
 on Ax^r + By^q = Cz^p using modularity of abelian varieties of GL2-type ov
 er totally real fields. However\, this program relies on various hard conj
 ectures\, making it impractical\, and until recently it has been successfu
 lly applied only in cases where the abelian varieties were elliptic curves
 . In this ta lk\, we will first discuss the limitations of the classical m
 odular method and some of the main ideas and issues of the Darmon program.
  Finally\, we will discuss an application to the equation x^7 + y^7 = 3 z^
 p.\n\nhttps://math-events.uni-bonn.de/event/246/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/246/
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