Zilber's conjecture on intersection with tori

Let $V\subseteq (\mathbb{C}^{\times})^n$ be an algebraic variety. Atypical subvarieties are the components of intersections with algebraic subtori having larger-than-expected dimension, and a maximal atypical subvariety is one maximal under inclusion. Zilber's conjecture on intersection with tori. Every algebraic variety in $(\mathbb{C}^{\times})^n$ contains only finitely many maximal atypical subvarieties. This is a diophantine finiteness conjecture generalising phenomena such as Mordell–Lang and Manin–Mumford; it is wide open, although many special cases are known.