**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.