The topology of complete spaces with nonnegative Ricci curvature.
Abstract. While there have been many advances in the understanding of the topology of complete noncompact manifolds of nonnegative Ricci curvature, this area is wide open for further study. In particular, Milnor's famous 1969 conjecture that such a manifold has a finitely generated fundamental group is still open. The speaker will survey a number of theorems and examples, including her work with Zhongmin Shen classifying the codimension one integer homology of these manifolds and her proof of the Milnor Conjecture when the manifolds are assumed to have small linear diameter growth. Unlike the algebraic approach in Burkhard Wilking's reduction of the Milnor conjecture to manifolds with abelian fundamental groups and the analytic proof by Shing-Tung Yau that a manifold with positive Ricci curvature has trivial codimension one real homology, the proofs of these results are purely geometric and can be described with a few key diagrams and lemmas.