# Donut choirs and Schiemann's symphony: An imaginative investigation of the isospectral problem for flat tori

@inproceedings{Nilsson2021DonutCA, title={Donut choirs and Schiemann's symphony: An imaginative investigation of the isospectral problem for flat tori}, author={Erik Nilsson and Julie Rowlett and Felix Rydell}, year={2021} }

Flat tori are among the only types of Riemannian manifolds for which the Laplace eigenvalues can be explicitly computed. In 1964, Milnor used a construction of Witt to find an example of isospectral non-isometric Riemannian manifolds, a striking and concise result that occupied one page in the Proceedings of the National Academy of Science of the USA. Milnor’s example is a pair of 16-dimensional flat tori, whose set of Laplace eigenvalues are identical, in spite of the fact that these tori are…

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