Raffaella Mulas

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.

Mathematicians are often seen through a lens of stereotypes: logical, detached thinkers who live in a world of abstract concepts, numbers, and formulas. These perceptions can make mathematics—and mathematicians—seem distant, unapproachable, or even intimidating. But they only scratch the surface. Mathematicians are as diverse, vibrant, and human as anyone else, with personal stories, creative pursuits, struggles, and achievements that shape both their lives and their work. This book brings together a selection of interviews that aim to go beyond the stereotypes and show the human side of mathematics. Each conversation offers a glimpse into the unique experiences, challenges, and passions of a different mathematician. These stories touch on the pursuit of knowledge, the balance between personal and professional life, reflections on mental health, and the central role of creativity in their work. Together, these voices show that mathematics is not only about logic and precision, but it is also shaped by diverse and often surprising perspectives.