Bailey R. Groups and Graphs, Designs and Dynamics 2024

Textbook in PDF format

This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.
Preface
Topics in representation theory of finite groups
Quantum probability approach to spectral analysis of growing graphs
Laplacian eigenvalues and optimality
Symbolic dynamics and the stable algebra of matrices
Author Index
Subject Index