Spectra of Discrete Structures - Jost, Jürgen; Mulas, Raffaella; Zhang, Dong
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Erscheint vorauss. 31. März 2026
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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 due to the discovery of Laplace operators that can probe their structure, and their manifold applications from chemical reaction networks to social interactions, they now constitute one of the hottest topics of interdisciplinary research. The authors' analysis of spectra of discrete structures embeds intuitive and easily visualized…mehr

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Produktbeschreibung
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 due to the discovery of Laplace operators that can probe their structure, and their manifold applications from chemical reaction networks to social interactions, they now constitute one of the hottest topics 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 which 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.
Autorenporträt
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.