Zilber's Restricted Trichotomy Conjecture predicts that every sufficiently rich strongly minimal structure which can be interpreted from an algebraically closed field K, must itself interpret K. Progress toward this conjecture began in 1993 with the work of Rabinovich, and recently Hasson and Sustretov gave a full proof for structures with universe of dimension 1. In this talk I will discuss a partial result in characteristic zero for universes of dimension greater than 1: namely, the conjecture holds in this case under certain geometric restrictions on definable sets. Time permitting, I will discuss how this result implies the full conjecture for expansions of abelian varieties.