From self-similar groups to self-similar sets and spectra

TL;DR

This survey explores how the theory of self-similar groups advances understanding of fractal sets, graphs, and their spectra, highlighting recent developments and applications.

Contribution

It provides a comprehensive overview connecting self-similar groups with fractal geometry and spectral theory, emphasizing new insights and applications.

Findings

Self-similar groups model fractal structures effectively.

Applications include analysis of fractal spectra and graphs.

The theory bridges algebraic and geometric perspectives.

Abstract

The survey presents developments in the theory of self-similar groups leading to applications to the study of fractal sets and graphs, and their associated spectra.