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SUMMARY:Jerson Caro (Boston University)
DTSTART:20250127T210000Z
DTEND:20250127T220000Z
DTSTAMP:20260423T040044Z
UID:NTBU/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTBU/16/">Ra
 tional points: Curves and beyond</a>\nby Jerson Caro (Boston University) a
 s part of Boston University Number Theory Seminar\n\nLecture held in CDS R
 oom 365 in Boston University.\n\nAbstract\nIn 1985\, Coleman\, building on
  Chabauty's work from 1941\, established an upper bound for the number of 
 rational points of curves satisfying certain conditions. In this talk\, I 
 will present the first generalization of this method to higher dimensions\
 , specifically to the case of surfaces. This is joint work with Hector Pas
 ten. Furthermore\, I will discuss recent work with Jennifer Balakrishnan\,
  in which we provide explicit examples of surfaces that demonstrate the ef
 fectiveness of the method developed by H. Pasten and me. Specifically\, we
  show that there are surfaces for which the obtained bound is sharp.\n\nFi
 nally\, I will present joint work with Natalia García-Fritz\, where we pr
 ove that a certain family of surfaces has a uniformly bounded number of ra
 tional points. In other words\, the same upper bound applies to all surfac
 es in the family.\n
LOCATION:https://researchseminars.org/talk/NTBU/16/
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