Spectral variation bounds in hyperbolic geometry

Lorentzian spectral geometry for globally hyperbolic surfaces

The fermionic signature operator is analyzed on globally hyperbolic Lorentzian surfaces. The connection between the spectrum of the fermionic signature operator and geometric properties of the surface is studied. The findings are illustrated by simple examples and counterexamples.

Spectral Variation Bounds for Diagonalisable Matrices

This note is related to an earlier paper by Bhatia, Davis, and Kittaneh 4]. For matrices similar to Hermitian, we prove an inequality complementary to the one proved in 4, Theorem 3]. We also disprove a conjecture made in 4] about the norm of a commutator.

Spectral Variation, Normal Matrices, and Finsler Geometry

Topological vertex, string amplitudes and spectral functions of hyperbolic geometry

We discuss the homological aspects of the connection between quantum string generating function and the formal power series associated to the dimensions of chains and homologies of suitable Lie algebras. Our analysis can be considered as a new straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of SL(2,Z)) to the partition...

Sharp Bounds on the PI Spectral Radius

In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.