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Spectral geometry - from the 19th to 21st century in 50 minutes

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Spectral geometry - from the 19th to 21st century in 50 minutes
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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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I will give a very pedestrian overview of some problems in spectral geometry — a vast topic covering relations between eigenvalues of boundary value problems for the Laplacian (or for other differential operators) in a Euclidean domain or on a Riemannian manifold, and the underlying geometry. They will include some open problems of various degrees of difficulty.