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SUMMARY:Unlikely intersections in families of abelian varieties and some p
 olynomial Diophantine equations - Laura Capuano (University of Oxford)
DTSTART:20171017T133000Z
DTEND:20171017T143000Z
UID:TALK76321@talks.cam.ac.uk
CONTACT:Beth Romano
DESCRIPTION:What makes an intersection likely or unlikely? A simple dimens
 ion count shows that two varieties of dimension r and s are non "likely" t
 o intersect if r < codim s\, unless there are some special geometrical rel
 ations among them. A series of conjectures due to Bombieri-Masser-Zannier\
 , Zilber and Pink rely on this philosophy. After a small survey on these p
 roblems\, I will speak about a joint work with F. Barroero (Basel) in this
  framework in the special case of curves in families of abelian varieties.
  This gives also applications to the study of the solvability of the so ca
 lled "almost-Pell" equations\, generalising some results due to Masser and
  Zannier. 
LOCATION:MR13
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