Laura Capuano, Oxford

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 28, 3:00-3:50

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.