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Daily Overview |
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DG1: Differential Geometry Location: A704 Session Chair: Oliver Schnürer Session Chair: Miles Simon | |
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Spectral theory on naturally reductive homogeneous spaces - theory and experiments Philipps-Universität Marburg, Germany The explicit computation of the spectrum of the Laplacian on closed Riemannian manifolds is a challenging task that only succeeds under strong symmetry assumptions. After the classical examples of spheres, projective spaces, and flat tori, Riemannian symmetric spaces G/K were the first large class of manifolds for which the spectrum could be computed explicitly via representation theoretic tools. For homogeneous non-symmetric spaces, the classical approaches fail. I will give an introduction to new methods for computing spectra on large families of naturally reductive homogeneous metrics. Many examples like Aloff-Wallach manifolds or Berger spheres will be used to illustrate the results; in fact, explicit spectra were computed using Python and are available as a Jupyter notebook. This is joint work with Jonas Henkel and Leandro Cagliero. | |
