2 options
Spectra of discrete structures / Jürgen Jost, Raffaella Mulas, Dong Zhang.
- Format:
- Book
- Author/Creator:
- Jost, Jürgen, 1956- Author.
- Mulas, Raffaella, 1992- author.
- Zhang, Dong (Of Beijing da xue), author.
- Series:
- Cambridge studies in advanced mathematics ; 221.
- Cambridge studies in advanced mathematics ; 221
- Language:
- English
- Subjects (All):
- Discrete mathematics.
- Spectral theory (Mathematics).
- Physical Description:
- 1 online resource (xvii, 406 pages) : digital, PDF file(s).
- Edition:
- 1st ed.
- Place of Publication:
- Cambridge ; New York, NY : Cambridge University Press, 2026.
- Summary:
- Addressing the active and challenging field of spectral theory, this book develops the general theory of spectra of discrete structures, on graphs, simplicial complexes, and hypergraphs. In fact, hypergraphs have long been neglected in mathematical research, but because of the discovery of Laplace operators that can probe their structure, and their manifold applications from chemical reaction networks to social interactions, they have now become one of the most active areas of interdisciplinary research. The authors' analysis of spectra of discrete structures embeds intuitive and easily visualized examples, which are often quite subtle, within a general mathematical framework. They highlight novel research on Cheeger-type inequalities that connect spectral estimates with the geometry, more precisely the cohesion, of the underlying structure. Establishing mathematical foundations and demonstrating applications, this book will be of interest to graduate students and researchers in mathematics working on the spectral theory of operators on discrete structures.
- Contents:
- The abstract setting
- The classical case
- First properties of the spectrum
- Floer theory
- Lovász extensions
- Discrete p-Laplacians
- Cheeger inequalities
- Nodal domains
- Interlacing and spectral classes
- Spectral theory of hypergraphs via tensors
- The non-backtracking Laplacian
- Applications.
- Notes:
- Title from publisher's bibliographic system (viewed on 29 May 2026).
- ISBN:
- 1-009-64182-4
- 9781009641852
- Access Restriction:
- Open Access. Unrestricted online access
The Penn Libraries is committed to describing library materials using current, accurate, and responsible language. If you discover outdated or inaccurate language, please fill out this feedback form to report it and suggest alternative language.