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SUMMARY:Ziyang Gao
DTSTART:20201014T150000Z
DTEND:20201014T160000Z
DTSTAMP:20260418T064636Z
UID:LNTS/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/14/">Bo
 unding the number of rational points on curves</a>\nby Ziyang Gao as part 
 of London number theory seminar\n\n\nAbstract\nMazur conjectured\, after F
 altings’s proof of the Mordell conjecture\, that the number of rational 
 points on a curve of genus g at least 2 defined over a number field of deg
 ree d is bounded in terms of g\, d and the Mordell-Weil rank. In particula
 r the height of the curve is not involved. In this talk I will explain how
  to prove this conjecture and some generalizations. I will focus on how fu
 nctional transcendence and unlikely intersections are applied in the proof
 . If time permits\, I will talk about how the dependence on d can be furth
 ermore removed if we moreover assume the relative Bogomolov conjecture. Th
 is is joint work with Vesselin Dimitrov and Philipp Habegger.\n
LOCATION:https://researchseminars.org/talk/LNTS/14/
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