Strongly minimal sets, i.e. irreducible sets of dimension one,
were first identified as the principal component of any uncountably
categorical structure by Michael Morley in his proof of Los' uncountable
categoricity conjecture. They were subsequently recognized to be the
main building block of any structure of finite Morley rank; Boris Zilber
conjectured that they fall essentially into one of three well-known
types. This was refuted by an ingenious construction of Hrushovski,
which is the principal tool of creating exotic strongly minimal sets.
The talk will be mostly oriented to an audience not familiar with Model
Theory, based on examples to illustrate the results exhibited.