# 2008

# Eigenmodes of a Laplacian on Laakso Space

# Eigenmodes of a Laplacian on Laakso Space

## Contributors

Kevin Romeo and Benjamin Steinhurst

## Overview

This group analyzed the spectrum of a self-adjoint operator on a Laakso space using the projective limit construction originally given by Barlow and Evans. They used the hierarchical cell structure induced by the choice of approximating quantum graphs to calculate the spectrum with multiplicities. They then extended the method for using the hierarchical cell structure to more general projective limits beyond Laakso spaces.

## Publications

Complex Variables and Elliptic Equations: An International Journal

arXiv.org

# Vibration Spectra of the m-Tree Fractal

## Contributors

Daniel Ford and Benjamin Steinhurst

## Overview

This group introduced a family of post-critically finite fractal trees indexed by the number of branches they possess. They then produced a Laplacian operator on graph approximations to these fractals and used spectral decimation to describe the spectrum of the Laplacian on these trees. Lastly they considered the behavior of the spectrum as the number of branches increases.