Zilber proposes at least two different but potentially complementary ways to regard strongly minimal structures or, more generally structures of finite Morley rank, as geometric.
I mention first, even though it is chronologically the second of his suggestions, the suggestion that the "field-like" strongly minimal sets may be understood in terms of string theory in the sense of mathematical physics or more mathematically, non-commutative algebraic geometry. Zilber has released a short note explaining how the counterexample to bi-interpretability with the field for Zariski geometries might be seen as a non-commutative space. At the moment, the details are hazy to me, but given Zilber's track record, there is reason to be optimistic that these speculations may lead to theorems. This story is changing constantly and you may wish to consult Zilber's website for the latest version.
Zilber noted some time ago that compact complex manifolds with their global analytic structure may be regarded as structures of finite Morley rank. In a compact complex manifold, every strongly minimal set (possibly after removing finitely many points) is a Zariski geometry. So, while this class contains interesting examples of strongly minimal structures, one cannot find a counterexample to the trichotomy within it.
Regard (C, +, ×, exp, 0, 1) as a relational structure. Define a function δ on the set C of finite subsets of C by
Then Schanuel's Conjecture, a well-known and notoriously difficult conjecture of transcendental number theory, is precisely the assertion that C = C0.
From this remarkable coincidence, Zilber has suggested that the Hrushovski-Fraïssé structures may be realized as complex analytic spaces with the relations given by sets defined by the vanishing of analytic functions, or, perhaps, only by sets defined by some other clearly geometric condition. While this suggestion remains just that in almost every case, there are some cases where it has been implemented.