Ricci Curvature and Fundamental Group in Riemannian Manifolds - Lecture 2

Explore a one-hour mathematics lecture from the Hausdorff Center that delves into the relationship between Ricci curvature and fundamental groups in Riemannian manifolds, examining historical developments since the 1940s and their modern implications. Learn about the structural properties of fundamental groups in manifolds with nonnegative Ricci curvature, including concepts like polynomial growth and virtual nilpotency. Examine key examples that motivate these mathematical relationships, and master various methods for proving finite generation of fundamental groups, including Gromov's short generators and Sormani's linear growth theorem. Study the characteristics of spaces and manifolds with infinitely generated fundamental groups, understand gluing constructions that preserve nonnegative Ricci curvature, and analyze constructions that counter the Milnor conjecture.