Survey of isospectral homogeneous Riemannian manifolds

LAURET, EMILIO A.

São Paulo

Workshop; 6th TWAS Young Affiliate Network (TYAN) Thematic Workshop in Mathematics and 1st Advanced School in Mathematics; 2022

TWAS Young Affiliates Network

We will review several results on inverse spectral geometry in the setting of homogeneous Riemannian manifolds. Some key points will be Schueth's examples of continuous curves of isospectral left-invariant metrics on compact Lie groups, Sutton's construction of isospectral compact homogeneous Riemannian manifolds (as a generalization of Sunada-Pesce's method), and spectral isolation/uniqueness problems among $G$-invariant metrics on a fixed homogeneous space $G/K$.