Unlikely intersections in families of abelian varieties and some polynomial Diophantine equations

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• Laura Capuano (University of Oxford)
• Tuesday 17 October 2017, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Beth Romano.

What makes an intersection likely or unlikely? A simple dimension count shows that two varieties of dimension r and s are non “likely” to intersect if r < codim s, unless there are some special geometrical relations among them. A series of conjectures due to Bombieri-Masser-Zannier, Zilber and Pink rely on this philosophy. After a small survey on these problems, 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 called “almost-Pell” equations, generalising some results due to Masser and Zannier.

This talk is part of the Number Theory Seminar series.

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