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SUMMARY:Bjorn Poonen (MIT)
DTSTART:20220126T153000Z
DTEND:20220126T170000Z
DTSTAMP:20260423T041510Z
UID:Vinberg/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Vinberg/8/">
 Undecidability in number theory</a>\nby Bjorn Poonen (MIT) as part of The 
 Vinberg Lecture Series\n\n\nAbstract\nHilbert's tenth problem asked for an
  algorithm that\, given a\nmultivariable polynomial equation with integer 
 coefficients\, would\ndecide whether there exists a solution in integers. 
  Around 1970\,\nMatiyasevich\, building on earlier work of Davis\, Putnam\
 , and Robinson\,\nshowed that no such algorithm exists.  But the answer to
  the analogous\nquestion with integers replaced by rational numbers is sti
 ll unknown\,\nand there is not even agreement among experts as to what the
  answer\nshould be.  The second half of the lecture will explore some of t
 he\ntechniques from arithmetic geometry that have been used towards\nanswe
 ring this question and the related question for the ring\nof integers of a
  number field.\n
LOCATION:https://researchseminars.org/talk/Vinberg/8/
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