Geometry and Topology of Spaces with Ricci Curvature Bounded From Below

Graduate / Professional

This topics course introduces the geometry, analysis, and topology of spaces with Ricci curvature bounded from below. We begin with foundational results for smooth Riemannian manifolds, including volume comparison, splitting theorems, and Gromov compactness, and then study the structure of limit spaces and metric measure spaces with synthetic Ricci curvature lower bounds (such as RCD spaces). Emphasis is placed on the interaction between curvature, topology, and analysis, including rigidity, stability, and fundamental group behavior. The course is intended for graduate students with background in differential geometry and analysis. TTh 11:35am-12:50pm