Then the speaker will present recent results with Guofang Wei (UCSB). The main result states that if we have a converging sequence of compact manifolds with a uniform upper bound on diameter and lower bound on Ricci curvature, then their limit space has a universal cover. This universal cover is in fact a limit of special covers of the sequence of manifolds, which we call delta covers. Furthermore, eventually there are surjective maps from the fundamental groups of the manifolds to the group of deck transforms of the limit space's universal cover.
A preprint is available at http://comet.lehman.cuny.edu/~sormani/research/papers.html