Structure of manifolds with lower Ricci curvature bounds. Part I

This is a report on joint work with Vitali Kapovitch. Building on the work of Cheeger and Colding we study the convergence of manifolds with lower Ricci curvature bound to limit spaces. The main applications are structure results for the fundamental groups of such manifolds. The talk will be in two parts. The first part will contain an exposition of background material.