Isospectrality in Symmetric Spaces

Abstract: For a Riemannian manifold $(M,g)$, we define its spectrum as the spectrum of the Laplace–Beltrami operator $\Delta_g$. We say that two Riemannian manifolds are isospectral if their spectra are equal. A fundamental problem in spectral geometry is to describe the isospectral class of distinguishable Riemannian manifolds.

In this talk, we study two families of homogeneous metrics on the manifolds $\mathrm{SO}(2n+2)/\mathrm{U}(n+1)$ and $\mathrm{SU}(2n+2)/\mathrm{Sp}(n+1)$. Using Lie theoretical methods, we describe the spectrum of each metric within these families and establish results regarding spectral uniqueness. This research is conducted jointly with Emilio Lauret, PhD (Universidad Nacional del Sur, Argentina).

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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