### Abstract

(Joint work with Hrushovski and Peterzil). I will give a proof of the conjectures relating [definably compact groups definable in saturated o-minimal expansion of RFC], to [compact Lie groups]. I will expand on some of the ingredients of the proof and related notions which may be of independent interest (Keisler's work on measures, consequences of "not the independence property", model theory of the standard part map,...)