Unlikely intersections in Shimura varieties and abelian varieties

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• Martin Orr (UCL)
• Tuesday 21 January 2014, 16:15-17:15
• MR13.

If you have a question about this talk, please contact James Newton.

The Manin-Mumford conjecture, which is a theorem of Raynaud, states that a curve of genus at least 2 in an abelian variety contains only finitely many torsion points. Analogues of this, such as the André-Oort and Zilber-Pink conjectures, have been stated for Shimura varieties in place of abelian varieties. In their most general form these imply many Diophantine results such as the Mordell-Lang conjecture. In this talk I will outline these conjectures and discuss one method of attacking them, due to Pila and Zannier and using results from model theory. In particular I will apply this method to a problem about curves in the moduli space of principally polarised abelian varieties.

This talk is part of the Number Theory Seminar series.

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