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SUMMARY:Generalized Fermat equations over totally real fields [MPIM]
DTSTART:20250212T133000Z
DTEND:20250212T143000Z
DTSTAMP:20260415T104600Z
UID:indico-event-245@math-events.uni-bonn.de
DESCRIPTION:Speakers: Diana Mocanu (MPIM)\n\nNumber theory lunch seminar\n
 Wiles’ famous proof of Fermat’s Last Theorem pioneered the so-called m
 odular method\, in which modularity of elliptic curves is used to show tha
 t all integer solutions of the Fermat’s equation are trivial.\nIn this t
 alk\, we briefly sketch a variant of the modular method described by Freit
 as and Siksek in 2014\, proving that for sufficiently large exponents\, Fe
 rmat’s Last Theorem holds in five-sixths of real quadratic fields. We th
 en extend this method to explore solutions to two broader Fermat-type fami
 lies of equations. The main ingredients are modularity\, level lowering\, 
 image of inertia comparisons\, and S-unit equations.\n\nhttps://math-event
 s.uni-bonn.de/event/245/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/245/
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