## Group Members

Courtney George, Samantha Jarvis.

## Supervisors

Dan Kelleher, Luke Rogers, Sasha Teplyaev.

## Overview

We analyze the spectra of a sequence of graphs constructed from the Schreier graphs of the Basilica group. Our analysis differs from earlier work of Grigorchuk and Zuk in that it is based on a macroscopic decomposition of the graphs. This method gives precise information about the multiplicities of eigenvalues and, consequently, good information about the spectral measures of large graphs. It also permits a proof of the existence of gaps in the spectrum of limiting graphs.