Compactness of isospectral sets
Typical surfaces and random graphs
Isospectral graphs and isospectral surfaces
On the Spectrum of Non-Compact Manifolds with Finite Volume.
A Relation Between Growth and the Spectrum of the Laplacian.
Injectivity radius and low eigenvalues of hyperbolic manifolds.
The bottom of the spectrum of a Riemannian covering.
On branched coverings of 3-manifolds which fiber over the circle.
The fundamental group and the spectrum of the Laplacian.
On the angles between certain arithmetically defined subspaces of
If and are two families of unitary bases for , and is a fixed number, let and be subspaces of spanned by vectors in and respectively. We study the angle between and as goes to infinity. We show that when and arise in certain arithmetically defined families, the angles between and may either tend to or be bounded away from zero, depending on the behavior of an associated eigenvalue problem.
Non-Sunada graphs
We consider the question of whether there is a converse to the Sunada Theorem in the context of -regular graphs. We give a weak converse to the Sunada Theorem, which gives a necessary and sufficient condition for two graphs to be isospectral in terms of a Sunada-like condition, and show by example that a strong converse does not hold.
The first eigenvalue of a Riemann surface.
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