Workshop on Topology: Identifying Order in Complex Systems

Fitting manifolds to data

The problems come in two flavors.

Extrinsic Flavor: Given a point cloud in R^N sampled from an unknown probability density, how can we decide whether that probability density is concentrated near a low-dimensional manifold M with reasonable geometry? If such an M exists, how can we find it? (Joint work with S. Mitter and H. Narayanan)

Intrinsic Flavor: How can we decide whether a given finite metric space is approximately isometric (in an appropriate sense) to an epsilon-net in a manifold M with reasonable geometry? If such an M exists, how can we find it?

(Joint work with S.Ivanov, Y. Kurylev, M. Lassas and H. Narayanan)

Date & Time

April 07, 2018 | 1:30pm – 2:30pm

Location

Simonyi Hall 101

Speakers

Charlie Fefferman

Affiliation

Princeton University

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