EUCLIDEAN VERSUS NON-EUCLIDEAN ASPECTS IN SPECTRAL GEOMETRY

The aim of this note is to give a survey of recent studies on spectra geometry. In the course of discussion, we put an emphasis on relationships between discrete group actions and the spectra of the Laplacian and magnetic Schrodinger operators on a non-compact Riemannian manifold. We employ typical models of geometry, the Euclidean plane and the non-Euclidean plane, to illustrate how group structures influence the spectra.