A survey of unlikely intersections in pure Shimura varieties, covering Andre-Oort, Andre-Pink-Zannier, Zilber-Pink, and the Pila-Zannier strategy.
Hodge loci and atypical intersections: conjectures
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abstract
We present a conjecture on the geometry of the Hodge locus of a (graded polarizable, admissible) variation of mixed Hodge structure over a complex smooth quasi-projective base, generalizing to this context the Zilber-Pink Conjecture for mixed Shimura varieties (in particular the Andr\'e-Oort conjecture).
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Unlikely intersections in Shimura varieties and beyond: a survey
A survey of unlikely intersections in pure Shimura varieties, covering Andre-Oort, Andre-Pink-Zannier, Zilber-Pink, and the Pila-Zannier strategy.