## View abstract

### Session S33 - Spectral Geometry

Tuesday, July 13, 12:00 ~ 12:20 UTC-3

## Do the Hodge spectra detect orbifold singularities?

### Carolyn Gordon

We will address the question: Does the spectrum of the Hodge Laplacian on $p$-forms distinguish closed Riemannian orbifolds with singularities from smooth Riemannian manifolds? This question remains open in the case of the Laplace-Beltrami operator (i.e., the case $p=0$), although many partial results are known. We show that the spectra of the Hodge Laplacians on functions and 1-forms together distinguish manifolds from orbifolds with sufficiently large singular set. We also obtain weaker affirmative results for the spectrum on 1-forms alone and show via counterexamples that some of these results are sharp.