BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Application of (mixed) Ax-Schanuel to counting rational points on 
 curves - Ziyang Gao
DTSTART:20190219T143000Z
DTEND:20190219T153000Z
UID:TALK118309@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:With Philipp Habegger we recently proved a height inequality\,
 \nusing which (and previous work of Rémond in the realm of the classical\
 nBombieri-Faltings-Vojta method) one can prove that the number of\nrationa
 l points on a 1-parameter family of curves of genus g is bounded\nin terms
  of g\, degree of the field\, the family and the Mordell-Weil rank\nof eac
 h individual curve in this family. In this talk I’ll explain how\nthe he
 ight inequality yields this bound\, and then explain how this\nmethod can 
 be generalized to an arbitrary family via mixed Ax-Schanuel\nfor universal
  abelian varieties. This is work in progress\, joint with\nVesselin Dimitr
 ov and Philipp Habegger.\n
LOCATION:MR13
END:VEVENT
END:VCALENDAR