Laura Capuano

Given n independent points on the Legendre family of elliptic curves of equation Y^2=X(X-1)(X-c) with coordinates algebraic over Q(c), 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 specialized curve. This fits in the framework of the so-called Unlikely Intersections. We will then see an higher-dimensional analogue of this result and explain how it applies to the problem of studying the solvability of the (almost-)Pell equation in polynomials.

This is joint work with Fabrizio Barroero.