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SUMMARY:Robin Zhang (MIT)
DTSTART:20251209T210000Z
DTEND:20251209T220000Z
DTSTAMP:20260824T074154Z
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 Pioneer Valley Number Theory Seminar\
 n\nLecture held in Seeley Mudd 207 @Amherst College.\n\nAbstract\nHow can 
 the finite/infinite dichotomy of the Killing–Cartan classification of si
 mple Lie groups & algebras appear in number theory? I will explain how thi
 s Lie-theoretic dichotomy is realized in the finiteness or infinitude of p
 ositive integer solutions to certain Diophantine equations and explore som
 e of its implications for classical questions studied by Gauss\, Mordell\,
  Coxeter\, Conway\, and Schinzel in combinatorics and number theory. I wil
 l then switch gears to the arithmetic dynamics of cluster Donaldson–Thom
 as transformations\, which refines the Diophantine realization of the fini
 te/infinite dichotomy into a finite/affine/indefinite trichotomy that matc
 hes the Kac–Moody classification of infinite-dimensional Lie algebras.\n
LOCATION:https://researchseminars.org/talk/FCNTS/15/
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