# 2009

# Modified Hanoi Towers Groups and Limit Spaces

# Spectrum and Heat Kernel Asymptotics on General Laakso Spaces

## Contributors

Matthew Begue, Levi deValve, David Miller, and Benjamin Steinhurst

## Overview

This group introduced a method of constructing a general Laakso space while calculating the spectrum and multiplicities of the Laplacian operator on it. Using this information, they found the leading term of the trace of the heat kernel of a Laakso space and its spectral dimension.

## Publications

# Modified Hanoi Towers Groups and Limit Spaces

## Contributors

Shotaro Makisumi, Grace Stadnyk, and Benjamin Steinhurst

## Overview

This group introduced the k-peg Hanoi automorphisms and Hanoi self-similar groups, a generalization of the Hanoi Towers groups, and gave conditions for them to be contractive. They analyzed the limit spaces of a particular family of contracting Hanoi groups, and showed that these are the unique maximal contracting Hanoi groups under a suitable symmetry condition. Finally, they provided partial results on the contraction of Hanoi groups with weaker symmetry.

## Publications

arXiv.org

International Journal of Algebra and Computation (IJAC)