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VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20221121T081127Z
DTSTART:20221206T150000Z
DTEND:20221206T160000Z
SUMMARY:Manchester Number Theory Seminar - Kostas Karagiannis
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u-m5iz8s
DESCRIPTION:Speaker: Kostas Karagiannis (University of Manchester)\n\nTit
le: The Galois module structure problem for Fermat curves\n\nAbstract:
The function field analogy is a general principle that states that the b
ehavior of number fields has striking similarities to that of transcende
ntal extensions of finite fields. The latter arise naturally as function
fields of algebraic curves\, thus giving a geometric flavor to Galois t
heory. In this talk\, I will discuss how tools from representation theor
y can be implemented into the context of Galois theory of curves\, focus
ing on automorphism groups of Fermat curves. The need for explicit calcu
lations leads to sums of roots of unity that resemble Kloosterman sums\,
giving an unexpected connection to analytic number theory. Time permitt
ing\, I will discuss how the subject fits into the general framework\, b
y introducing equivariant versions of classic algebro-geometric invarian
ts\, such as Euler characteristics and Hilbert functions.\n\nRoom: Frank
Adams 1
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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