Groups and Graphs, Designs and Dynamics

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.

• Provides an in-depth look at four important mathematical topics emphasizing their common roots in linear algebra
• Features numerous exercises in each chapter rounding out the theory
• All chapters can be read independently but contain many cross-references and commonalities