Spectral geometry and symmetries

Abstract: We will present two short results linking the spectrum of the Laplace-Beltrami operator on a compact Riemannian manifold to its Lie group of isometries:

(1) Each manifold with a simple Laplace-Beltrami spectrum has a finite isometry group. (https://arxiv.org/abs/2407.18797)

(2) If a two-dimensional drumhead "sounds the same" when struck at any two points, the action of the isometry group on the surface is transitive. (https://arxiv.org/abs/2307.06224)

We will discuss some background on Laplace-Beltrami eigenfunctions, give short proofs of the results, and discuss some further questions if time permits. This is joint work with Xing Wang, Feng Wang, and Yakun Xi.

differential geometryspectral theory

Audience: researchers in the topic

( paper | video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Differential geometry.

The seminar meets every other Wednesday. To accommodate most time zones, the time rotates. The Zoom link is sent to the mailing list around 24 hours before each talk. To subscribe to the mailing list, fill the following form: docs.google.com/forms/d/e/1FAIpQLSdKrJ-nivgjr7ZVJmIY0qkN-VbzTl5NHHNyg6nNsCqjhB-4WA/viewform?usp=sf_link.

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