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SUMMARY:Unlikely Intersections in certain families of abelian varieties an
 d the polynomial Pell equation - Fabrizio Barroero (University of Manchest
 er)
DTSTART:20160524T131500Z
DTEND:20160524T141500Z
UID:TALK65658@talks.cam.ac.uk
CONTACT:G. Rosso
DESCRIPTION:Given n independent points on the Legendre family of elliptic 
 curves of equation Y^2=X(X-1)(X-t) with coordinates algebraic over Q(t)\, 
 we will see that there are at most finitely many specializations of c such
  that two independent relations hold between the n points on the specializ
 ed curve. This fits in the framework of the so-called Unlikely Intersectio
 ns. We will then see an higher-dimensional analogue of this result and exp
 lain how it applies to the problem of studying the solvability of the (alm
 ost-)Pell equation in polynomials.\nThis is joint work with Laura Capuano.
LOCATION:MR13\, Centre for Mathematical Sciences
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