It was conjectured by John Milnor in 1968 that the fundamental group of a complete Riemannian manifold with nonnegative Ricci Curvature is finitely generated. I will present joint work with Elia Bruè and Aaron Naber where we construct a family of complete Riemannian manifolds with nonnegative Ricci Curvature and infinitely generated fundamental group, thus providing a counterexample to the Milnor conjecture.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/3050