Spectral Geometry and Finiteness Results for Orbifolds
by Emily Proctor and Liz Stanhope
Abstract: We begin with an overview of spectral geometry, including a summary of results regarding the interplay between Laplace spectrum of an orbifold and the geometry and topology of the orbifold. We briefly review several finiteness results for manifolds, and describe our proof that an isospectral set of two-orbifolds with sectional curvature uniformly bounded below contains orbifolds of only finitely many orbifold diffeomorphism types. Later in the talk, we describe our current work, which aims to show that an isospectral set of orbifolds (of any dimension) with sectional curvature bounded below contains only finitely many orbifold homotopy types.
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