Katie Gittins

Do the Hodge spectra distinguish orbifolds from manifolds?

A Riemannian orbifold can be thought of as a generalisation of a Riemannian manifold that has well-structured singularities. As these singularities are a key feature of an orbifold, a natural question is: ``can spectral data detect the presence of orbifold singularities?''
We focus on the Hodge Laplacian acting on differential forms on compact Riemannian orbifolds without boundary. We obtain a small-time asymptotic expansion for the heat trace in this setting and apply the heat invariants for differential forms to obtain some positive results in this direction. We also discuss some negative results by presenting counterexamples.
This is based on joint work with Carolyn Gordon, Magda Khalile, Ingrid Membrillo Solis, Juan Pablo Rossetti, Mary Sandoval, and Elizabeth Stanhope.