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SUMMARY:Ziyang Gao (CNRS & IMJ-PRG)
DTSTART:20201229T003000Z
DTEND:20201229T013000Z
DTSTAMP:20260423T024744Z
UID:iccm2020/92
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/iccm2020/92/
 ">Bounding the number of rational points on curves</a>\nby Ziyang Gao (CNR
 S & IMJ-PRG) as part of ICCM 2020\n\n\nAbstract\nMazur conjectured\, after
  Faltings’s proof of the Mordell conjecture\, that the number of rationa
 l points on a curve of genus g at least 2 defined over a number field of d
 egree d is bounded in terms of g\, d and the Mordell-Weil rank. In particu
 lar the height of the curve is not involved. In this talk I will explain h
 ow to prove this conjecture and some generalizations. I will focus on how 
 functional transcendence and unlikely intersections are applied in the pro
 of. If time permits\, I will talk about how the dependence on d can be fur
 thermore removed if we moreover assume the relative Bogomolov conjecture. 
 This is joint work with Vesselin Dimitrov and Philipp Habegger.\n
LOCATION:https://researchseminars.org/talk/iccm2020/92/
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