Mary Sandoval, Trinity College, Hartford, Connecticut

Title: Orbifold Singularities and Orbifold Length Spectra

Abstract: In this talk, we will consider the geodesic flow on a compact Riemannian orbifold O. Assuming the set of closed geodesics on the orbifold is non-empty, we consider the following question: Is it possible to detect orbifold singularities via the length spectrum of O and the length spectrum of the associated orthonormal frame bundle of the orbifold? The answer is a qualifed yes, provided that the closed geodesic flow on O intersects with the singular set of the orbifold, and the non-trivial isotropy group of the singularity "closes up" the geodesic. Assuming these conditions are satisfied, we consider a second question: Given a singularity on a closed geodesic, what aspects of the isotropy group can be determined from knowing all the closed geodesics that pass through the singularity? Partial results to this second question will be discussed. The proofs will use some recent results from the spectral theory of leaf spaces of regular and singular Riemannian foliations.