Do the wave invariants of a Riemannian orbifold detect its singular structure?
by Liz Stanhope
Abstract: The task of an inverse spectral geometer is to extract information about a manifold from the Laplace eigenvalue spectrum of that manifold. One way to do this is to study the wave invariants of a manifold. These invariants contain geometric information about the manifold and are determined by the manifold's Laplace spectrum.
In a recent project with Alejandro Uribe (Michigan), the question in the title of this talk was raised but not quite resolved. In the talk we will begin by looking at an example to become familiar with Riemannian orbifolds and their Laplace spectra. We'll then set up the analytic machinery that suggests an answer to this question might rely on the behavior of conjugacy classes in a Lie group.