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SUMMARY:Coarse Curvature - Xue Mei Li (Imperial College London)
DTSTART:20240906T123000Z
DTEND:20240906T131500Z
UID:TALK217648@talks.cam.ac.uk
DESCRIPTION:We introduce a novel concept of coarse extrinsic curvature for
  Riemannian submanifolds\, inspired by Ollivier's notion of coarse Ricci c
 urvature. This curvature is derived from the Wasserstein 1-distance betwee
 n probability measures supported in the tubular neighborhood of a submanif
 old\, providing new insights into the extrinsic curvature of isometrically
  embedded manifolds in Euclidean spaces. The framework also offers a metho
 d to approximate the mean curvature from statistical data\, such as point 
 clouds generated by a Poisson point process. This approach has potential a
 pplications in manifold learning and the study of metric embeddings\, enab
 ling the inference of geometric information from empirical data.
LOCATION:Seminar Room 1\, Newton Institute
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