Abstract: In this talk, we report on joint work in progress with Netan Dogra on the Zilber–Pink conjecture for curves inside abelian varieties, using a p-adic method. The Zilber–Pink conjecture can be viewed as a vast generalisation of well-known conjectures in Diophantine geometry, including the Mordell, Mordell–Lang, and André–Oort conjectures. We will begin with an overview of our approach in the context of Mordell–Lang for curves and discuss how it compares with that of Zilber–Pink.