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PRODID:-//Columba Systems Ltd//NONSGML CPNG/SpringViewer/ICal Output/3.3-
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CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20221019T143005Z
DTSTART:20221108T150000Z
DTEND:20221108T160000Z
SUMMARY:Manchester Number Theory Seminar - Pedro Cazorla Garcia
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}kfg-l8vge0x
4-fqz5mq
DESCRIPTION:Speaker: Pedro Cazorla Garcia (University of Manchester)\n\nT
itle: The generalised Lebesgue-Ramanujan-Nagell equation\n\nAbstract: T
he Lebesgue-Ramanujan-Nagell equation x^2 + D = y^n has been studied ext
ensively by number theorists during the last century\, both by its intri
nsic interest and as a generalisation to Catalan's conjecture. With the
advent of the modular methodology developed by Wiles\, Ribet and others
and employed in the proof of Fermat's last theorem\, along with the evol
ution of computational number theory techniques\, it is now feasible to
consider the generalised Lebesgue-Ramanujan-Nagell equation C1x^2 + C2 =
y^n. \n\nIn this talk\, we will discuss a variety of techniques which a
llow us to solve the aforementioned equation in the range 1 <= C1\, C2 <
= 20\, involving the modularity of Galois representations and Thue equat
ions. All of this is joint work with Vandita Patel.\n\nRoom: Frank Adams
1
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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