Groups and Graphs, Designs and Dynamics

A collection of four short courses on group representations, graph eigenvalues, statistical optimality, and symbolic dynamics.

R. A. Bailey (Edited by), Peter J. Cameron (Edited by), Yaokun Wu (Edited by)

9781009465953, Cambridge University Press

Paperback / softback, published 30 May 2024

450 pages
22.9 x 15.3 x 2.4 cm, 0.63 kg

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.

1. Topics in representation theory of finite groups Tullio Ceccherini-Silberstein, Fabio Scarabotti and Filippo Tolli
2. Quantum probability approach to spectral analysis of growing graphs Nobuaki Obata
3. Laplacian eigenvalues and optimality R. A. Bailey and Peter J. Cameron
4. Symbolic dynamics and the stable algebra of matrices Mike Boyle and Scott Schmieding
Author index
Subject index.

Subject Areas: Calculus & mathematical analysis [PBK]