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SUMMARY:Robin Zhang (MIT)
DTSTART:20251209T210000Z
DTEND:20251209T220000Z
DTSTAMP:20260422T173918Z
UID:FCNTS/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FCNTS/15/">A
  Lie-theoretic trichotomy in Diophantine geometry and arithmetic dynamics<
 /a>\nby Robin Zhang (MIT) as part of Five College Number Theory Seminar\n\
 nLecture held in Seeley Mudd 207 @Amherst College.\n\nAbstract\nHow can th
 e finite/infinite dichotomy of the Killing–Cartan classification of simp
 le Lie groups & algebras appear in number theory? I will explain how this 
 Lie-theoretic dichotomy is realized in the finiteness or infinitude of pos
 itive integer solutions to certain Diophantine equations and explore some 
 of its implications for classical questions studied by Gauss\, Mordell\, C
 oxeter\, Conway\, and Schinzel in combinatorics and number theory. I will 
 then switch gears to the arithmetic dynamics of cluster Donaldson–Thomas
  transformations\, which refines the Diophantine realization of the finite
 /infinite dichotomy into a finite/affine/indefinite trichotomy that matche
 s the Kac–Moody classification of infinite-dimensional Lie algebras.\n
LOCATION:https://researchseminars.org/talk/FCNTS/15/
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