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UID:a58d86472690d8b8175083d719aaa04f
CATEGORIES:Complex Analysis and Geometry Seminar
CREATED:20260206T215523
SUMMARY:An Explicit Uniform Bound for Rational Points on Curves
LOCATION:https://rutgers.zoom.us/j/93924804346?pwd=bvgNTkrmFHNwFTLLxgtajQw7XYaLNo.1
DESCRIPTION:The celebrated Mordell conjecture, proved by Faltings, asserts that a curve
  of genus greater than one over a number field has only finitely many ratio
 nal points. A deep uniform upper bound on the number of rational points fol
 lows from Vojta's inequality and the recent works of Dimitrov-Gao-Habegger 
 and Kühne. In this talk, I will introduce an explicit version of this unifo
 rm bound. Our approach relies on analyzing Arakelov Kähler forms via locali
 zation of Bergman kernels. This is joint work with Jiawei Yu and Xinyi Yuan
 .\n
X-ALT-DESC;FMTTYPE=text/html:<p><span data-olk-copy-source="MessageBody" style="font-size: 11pt; font-fa
 mily: Calibri, sans-serif; margin: 0px;">The celebrated Mordell conjecture,
  proved by Faltings, asserts that a curve of genus greater than one over a 
 number field has only finitely many rational points. A deep uniform upper b
 ound on the number of rational points follows from Vojta's inequality and t
 he recent works of Dimitrov-Gao-Habegger and Kühne. In this talk, I will in
 troduce an explicit version of this uniform bound. Our approach relies on a
 nalyzing Arakelov Kähler forms via localization of Bergman kernels. This is
  joint work with Jiawei Yu and Xinyi Yuan.</span></p>
CONTACT:Shengxuan Zhou
DTSTAMP:20260826T211417
DTSTART;TZID=America/New_York:20260213T103000
DTEND;TZID=America/New_York:20260213T113000
SEQUENCE:0
TRANSP:OPAQUE
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