The Pila-Zannier Strategy for Drinfeld Modules

The Pila–Zannier strategy has proved to be a particularly fruitful approach: first applied to reprove the Manin–Mumford conjecture, it was later exploited decisively in proofs of the André–Oort conjecture. Crucially relying on a recent counting theorem of Binyamini–Kato specialized to function fields of positive characteristic, we extend this method to the setting of Drinfeld modules, thereby (re)proving certain cases of these conjectures. Joint work in progress with Gal Binyamini and Dmitry Novikov.