Logic Colloquium 2008
Amador Martin-Pizarro Categoricity and the classification of strongly minimal sets.
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.