Abstract: We will compare spectral data (eigenvalues of Hodge Laplacians acting on p-forms) of compact flat manifolds M with geometric and topological properties of M. We will discuss some recent results concerning the p-form spectra and the length spectra (collection of lengths of closed geodesics) on M. We will also show there are compact flat manifolds that are strongly isospectral but have non-isomorphic cohomology rings.
This talk will be accessible to graduate students.