Pregeometries and definable groups

We describe a recent program for analyzing definable sets and groups in certain model theoretic settings. Those settings include:(a) o-minimal structures (M, P), where M is an ordered group and P is a real closed field defined on a bounded interval (joint work with Peterzil),(b) tame expansions (M, P) of a real closed field M by a predicate P, such as expansions with o-minimal open core (work in progress with Gunaydin and Hieronymi).The analysis of definable groups first goes through a local level, where a pertinent notion of a pregeometry and generic elements is each time introduced.