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SUMMARY:Nicole Looper (Brown)
DTSTART:20261013T203000Z
DTEND:20261013T213000Z
DTSTAMP:20261023T093553Z
UID:MITNT/144
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/144/">
 Potential theory\, ultrafilters\, and uniform boundedness of rational tors
 ion on abelian varieties</a>\nby Nicole Looper (Brown) as part of MIT numb
 er theory seminar\n\nLecture held in Room 2-449 in the Simons Building (bu
 ilding 2).\n\nAbstract\nIn 1996\, building off of prior work by Mazur and 
 Kamienny\, Merel proved his famous theorem on the uniform boundedness of t
 he $K$-rational torsion of an elliptic curve over a number field $K$. The 
 (strong) Torsion Conjecture generalizes this theorem to abelian varieties 
 of arbitrary dimension: it states that given any positive integers $g$ and
  $N$\, there is a $B=B(g\,N)$ such that for any $g$-dimensional abelian va
 riety $A$ over a number field $K$ satisfying $[K:\\mathbb{Q}]\\le N$\, the
  set of $K$-rational torsion points of $A$ has order at most $B$. In this 
 talk\, I will present a function field analogue of this conjecture as well
  as a sketch of its proof. This is joint work with Jit Wu Yap.\n
LOCATION:https://researchseminars.org/talk/MITNT/144/
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