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Unlikely Intersections in families of abelian varieties

Laura Capuano, Oxford
Tuesday, February 28, 2017 - 2:00pm
PDL C-36
Pre-Seminar
 
When: Tuesday February 28, 2:00--2:45
Where: PDL C-36
Speaker: Laura Capuano (Oxford)
 
Title:  Abelian varieties and Mordell-Lang conjecture
 
Abstract: 
In this talk, I will give a short review of some aspects of theory of abelian varieties and then try to motivate Mordell-Lang conjecture, showing especially how it generalizes the Mordell conjecture and the Manin-Mumford conjecture.
 
 
Seminar
 
When: Tuesday February 283:00-3:50
Where: PDL C-36
Speaker: Laura Capuano (Oxford)
 
Title:  Unlikely Intersections in families of abelian varieties
 
Abstract: 
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.
 
 
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