Geometry and Topology of Data

Explore the intersection of topological data analysis and geometric concepts in this 43-minute lecture by Jürgen Jost. Delve into the fundamental notion of hyperconvexity and its variants, leading to a new concept of generalized curvature for metric spaces. Discover how curvature notions, originating from Riemannian geometry, play a crucial role in metric geometry. Learn about the Riemann curvature tensor and its significance in encoding invariants of Riemannian metrics. Gain insights from joint work with Parvaneh Joharinad, connecting the basic concepts of topological data analysis, such as intersection patterns of distance balls, with geometric principles.