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Hearing the Shape of the Bunny

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Hearing the Shape of the Bunny
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22
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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It is well-known that one cannot generally hear the shape of a drum: the metric of a compact surface is not uniquely determined by its Laplace-Beltrami spectrum. But one can still seek computational solutions to the inverse problem: given a sequence of eigenvalues, can we compute a surface whose Laplace-Beltrami spectrum approximates the sequence? I will discuss some numerical experiments related to this problem for the case of surfaces of sphere topology, whose discrete conformal parameterization leads to an especially simple formulation of the inverse problem.