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Geometric Rigidity from Eigenfunction Triple Products

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GST - Geometric spectral theory and applications

Although a manifold cannot, in general, be recovered from its Laplace spectrum alone, it can be reconstructed from the spectrum together with the structure constants arising from triple products of eigenfunctions. It is therefore natural to ask what geometric information these structure constants encode. In this talk, we will review existing results in this direction, show that sufficiently sparse structure constants force flatness, and conclude with further conjectures.

This talk is part of the Isaac Newton Institute Seminar Series series.

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