Expanders, Eigenvalues, and Related Topics

The topics of "expanders" and "graph eigenvalues" attract computer scientists, mathematicians, and physicists; these topics, while intrinsically interesting, also provide surprising and compelling connections between diverse fields.

An "expander" is a type of graph with good connectivity properties. We shall explain what "expanders" are and how the eigenvalues of a graph's adjacency matrix relate to "expansion".

We show that the study of "expanders" and "graph eigenvalues" includes a new Laplacian eigenvalue bound in Riemannian geometry and an approach to getting bounds on error-correcting codes.