Arithmetic jet spaces and the Zilber—Pink conjecture

The Zilber—Pink conjecture is a simultaneous generalisation of the Mordell—Lang conjecture and the Andre—Oort conjecture. In this talk, I will discuss new results concerning the Zilber—Pink conjecture for a subvariety of an abelian variety. The approach uses a version of Buium's theory of arithmetic jet spaces, and may be viewed as a generalisation of Buium's proof of the Manin—Mumford ​conjecture. This is joint work with Arnab Saha.