Francesco Maria Saettone, of the Weizmann Institute of Science, presents this Special Year Research Seminar at the Institute for Advanced Study on extending the Pila-Zannier strategy to Drinfeld modules. He traces the method's history, first used to reprove the Manin-Mumford conjecture and later deployed in proofs of the André-Oort conjecture, both results about special points on algebraic varieties. The talk's core is a recent counting theorem of Binyamini and Kato, specialized here to function fields of positive characteristic, which Saettone uses to carry the Pila-Zannier machinery into the Drinfeld module setting and reprove certain cases of the analogous conjectures there. He presents this as joint work in progress with Gal Binyamini and Dmitry Novikov, walking through the technical adaptations needed to move from number fields to function field arithmetic. The talk assumes familiarity with model theory and arithmetic geometry and is aimed at specialists following this research program.