Geometric stability theory

Abstract

These notes cover some of the foundational results of geometric stability theory. We focus on the geometry of minimal sets. The main aim is an account of Hrushovski's result that unimodular (in particular, locally finite or pseudofinite) minimal sets are locally modular; along the way, we discuss the Zilber trichotomy and the group and field configurations. We assume the basics of stability theory (forking calculus, U-rank, canonical bases, stable groups and homogeneous spaces), as can be found e.g. in Daniel Palacín's chapter in this volume [5].