Spectral theory of Laplace operators on oriented hypergraphs

Spectral Theory of Laplace and Schrödinger Operators (13w5059)

Geometrically sharp “isoperimetric” estimates on eigenvalues of the Laplacian and the Schrödinger operator help us understand how frequencies and energies of physical systems are constrained by the shape and size of the domain in which the physical process takes place. For example, the Faber–Krahn inequality (Rayleigh’s conjecture) tells us precisely how low the frequency of a drum can be, if t...

Spectral Asymptotics of Laplace Operators on Surfaces with Cusps

Ela Spectral Properties of Oriented Hypergraphs

An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of +1 or −1. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and Laplacian matrices of an oriented hypergraph which depend on structural parameters of the oriented hypergraph are found. An oriented hypergraph and its incidence dual are ...

On Spectral Theory of Quantum Vertex Operators

In this note we prove a conjecture from [DFJMN] on the asymptotics of the composition of n quantum vertex operators for the quantum affine algebra Uq(ŝl2), as n goes to ∞. For this purpose we define and study the leading eigenvalue and eigenvector of the product of two components of the quantum vertex operator. This eigenvector and the corresponding eigenvalue were recently computed by M.Jimbo....

The spectral geometry of operators of Dirac and Laplace type

Contents 1 Introduction 2 The geometry of operators of Laplace and Dirac type 3 Heat trace asymptotics for closed manifolds 4 Hearing the shape of a drum 5 Heat trace asymptotics of manifolds with boundary 6 Heat trace asymptotics and index theory 7 Heat content asymptotics 8 Heat content with source terms 9 Time dependent phenomena 10 Spectral boundary conditions 11 Operators which are not of ...