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SUMMARY:Bjorn Poonen (MIT)
DTSTART:20240321T200000Z
DTEND:20240321T213000Z
DTSTAMP:20260422T220136Z
UID:STAGE/103
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/103/">
 Siegel's method</a>\nby Bjorn Poonen (MIT) as part of STAGE\n\nLecture hel
 d in Room 2-131 in the MIT Simons Building.\n\nAbstract\nWe will show how 
 theorems about diophantine approximation (e.g.\, Roth's theorem that irrat
 ional algebraic numbers cannot be approximated too well by rational number
 s) can be used to prove one of the most famous theorems of 20th century ar
 ithmetic geometry\, Siegel's theorem that a hyperbolic affine curve can ha
 ve only finitely many integral points.  The proof is ineffective\, however
 : 95 years later it is still not known if there is an algorithm that takes
  as input the equation of a curve and returns the list of its integral poi
 nts.\n\nReference: Chapter 7 of Serre\, Lectures on the Mordell-Weil theor
 em.\n
LOCATION:https://researchseminars.org/talk/STAGE/103/
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