Geometry/topology Seminar
Tuesday, April 21, 2009, 4:30pm, 119 Physics
Mauro Maggioni (Duke)
Parametrizations of manifolds via Laplacian eigenfunctions and heat kernels
Abstract:- We present recent results that show that for any portion of a
compact manifold that admits a bi-Lipschitz parametrization by a Euclidean
ball one may find a well-chosen set of eigenfunctions of the Laplacian that
gives a bi-Lipschitz parametrization almost as good as the best possible. A
similar, and in some respect stronger result holds by replacing
eigenfunctions with heat kernels. These constructions are motivated by
applications to the analysis of the geometry of data sets embedded in
high-dimensional spaces, that are assumed to lie on, or close to, a
low-dimensional manifold. This is joint work with P.W. Jones and R. Schul. [video]
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