Mathematical Sciences Geometry/Topology Seminar

March 31:
Speaker: Craig Sutton (U.Penn)
Title: Methods of constructing isospectral manifolds

Abstract: Spectral geometry is the study of the interplay between the geometry of Riemannian manifold $(M,g)$ and the spectrum of its associated Laplace operator $\Delta : C^{\infty}(M) \to C^{\infty}(M)$. The literature is full of many examples of isospectral non-isometric manifolds and most of these can be explained by one of two construction methods: Sunada's method or the submersion method. In this talk we will review these two procedures and discuss some generalizations which give interesting examples of isospectral manifolds. We will also discuss a result due to Ballmann which unifies these two methods, thus showing they are each special cases of a more general phenomenon.