Geometries, Hrushovski constructions, and ampleness

Mondays 10-12 SR1d

WiSe2021/22 seminar run by Katrin Tent, assisted by Martin Bays and Blaise Boissonneau.

The motivation for the seminar is Zilber's Trichotomy Conjecture which stated that any strongly minimal set is *essentially* either a trivial structure, a vector space or an algebraically closed field where the dividing lines depend on the underlying geometry of the strongly minimal set.

We will introduce these geometries, define the different classes and then study the counterexample to this conjecture constructed by Hrushovski.

These new geometries arising from Hrushovski's counterexample give rise to a new hierarchy of a notion of ampleness which makes sense in general stable structures. We will study the ampleness hierarchy both in the context of free groups and in the context of omega-stable theories and theories of finite Morley rank.

If you are interested in participating, please contact Martin Bays <> or Katrin Tent.