Curvature Estimation for Point Clouds, Graphs, and Finite Metric Spaces
Presenter
May 20, 2026
Abstract
We introduce an estimator for the scalar curvature of a data set presented as a finite metric space (e.g., a distance matrix, a point cloud, or a graph with the shortest-path metric). Our estimator depends only on the metric structure of the data (not on an embedding in Euclidean space), and it converges to the ground-truth scalar curvature as the number of points increases. We'll close with a second approach to discrete scalar curvature, derived from Ollivier-Ricci curvature—an edge-based notion of discrete curvature for graphs. This is joint work with Andrew Blumberg.