New Book on Spectral Theory of Discrete Structures

Our emeritus director Jürgen Jost, together with our former PhD student and Minerva Group Leader Raffaella Mulas (now Assistant Professor at VU Amsterdam), and former postdoctoral researcher Dong Zhang (now Assistant Professor at Peking University), has co-authored the new book Spectra of Discrete Structures, published by Cambridge University Press as part of the Cambridge Studies in Advanced Mathematics series. The book develops a comprehensive spectral theory for discrete structures, including graphs, simplicial complexes, and hypergraphs.

While hypergraphs were long underexplored in mathematical research, recent advances—particularly the development of Laplace operators capable of probing their structure—have brought them to the forefront of interdisciplinary study. Today, they play an important role in applications ranging from chemical reaction networks to models of social interaction.

Combining rigorous mathematical foundations with intuitive and often visually accessible examples, the authors present a unified framework for understanding the spectra of discrete structures. Particular emphasis is placed on recent developments such as Cheeger-type inequalities, which establish connections between spectral properties and the geometry—or more precisely, the cohesion—of the underlying structures.

The book is intended for graduate students and researchers in mathematics, especially those working in spectral theory and its applications to discrete systems.

An open-access version of the book is available online, where printed copies can also be ordered.