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A central topic of recent study in arithmetic geometry has been to understand when families of algebraic varieties acquire extra algebraic structure that is in some sense "unlikely". The central conjecture in this area is the Zilber-Pink conjecture, of which the (recently resolved for Shimura varieties) Andre-Oort conjecture is a special case. In this talk we describe new results on the Zilber-Pink conjecture obtained via the theory of G-functions, and in addition give new results on the distribution of CM moduli beyond the setting of Shimura varieties.

DioG Program Research Seminar: G-Functions And Atypicality