Modular Andre-Oort with Derivatives

Haden Spence (Oxford)

Frank Adams 1 ,

I will discuss my recent work proving a conjecture of Jonathan Pila.  The conjecture is an Andre-Oort-type statement involving the modular function j and its first two derivatives.  It turns out to be approachable using a variant of the usual o-minimal strategy and the Pila-Wilkie Theorem, going via the theory of so-called "almost holomorphic" modular functions.  If time permits I will go on to discuss a stronger version of Pila's original conjecture, in which some unique new phenomena arise.

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