Spectra of Discrete Structures

Jürgen Jost is a founding Director and Scientific Member at the Max Planck Institute for Mathematics in the Sciences. He is a recipient of the Gottfried-Wilhelm-Leibniz award of the DFG (1993) and is a member of the German National Academy Leopoldina, the Academy of Science and Literature at Mainz, and the Saxonian Academy of Science at Leipzig. Raffaella Mulas is a tenured Assistant Professor at VU Amsterdam, where her research is supported by NWO VENI and VU Startpremie grants. Previously, she was a Group Leader at the Max Planck Institute for Mathematics in the Sciences, where her research group was supported by a Minerva Fast Track Fellowship from the Max Planck Society, and a postdoc at the Alan Turing Institute in London. Dong Zhang is an Assistant Professor at Peking University, and was previously a postdoctoral researcher at the Max Planck Institute for Mathematics in the Sciences. His research area is discrete analysis, especially nonlinear spectral graph theory and discrete-to-continuous extensions.

• Preface; Acknowledgments; Organization of the book; Part I. Basics: Foundational Material, Elementary Aspects, Examples: 1. Introduction; 2. The abstract setting; 3. The classical case; 4. First properties of the spectrum; 5. Floer theory; Part II. Eigenvalues and Eigenfunctions on Simplicial Complexes and Hypergraphs: 6. Lovász extensions; 7. Discrete p-Laplacians; 8. Cheeger inequalities; 9. Nodal domains; Part III. Additional topics: Interlacing, Tensors, Non-backtracking Laplacians, and Applications: 10. Interlacing and spectral classes; 11. Spectral theory of hypergraphs via tensors; 12. The non-backtracking Laplacian; 13. Applications; Bibliography; Index.