Topological analysis of topological insulators and political networks: an interdisciplinary study

Abstract

Topological data analysis is an emerging powerful data analysis tool inspired by algebraic topology. In this thesis I present my application of topological data analysis to the field of topological insulators and political networks.

In the context of topological insulators, I explored the potential of using topological data analysis in classifying topological phases in the extended Su-Schrieffer-Heeger (SSH) models, which are fundamental models describing the physical system in topological insulators. I show, in this study, the success of applying topological data analysis to the complex SSH model and the challenges in extending the method into non-Hermitian SSH models.

The application of topological data analysis to professional networks within Australian Parliament from 1947 to 2019 follows a different trajectory. The career background data is significantly more complex compared to the simulated data used in the study of SSH models. As such, the project is separated into two stages, understanding the professional networks using network theory, and the application of topological data analysis to these networks.

The analysis of these professional networks included summary statistics and random graph simulations of party-specific networks within the Australian Labor Party and Liberal Party. Through this analysis, we discovered an important structure within these association networks, the bouquet structures. I show how these structures can be used as a new centrality measure that opens up research opportunities for qualitative work. I also present ongoing work utilising Approximate Bayesian Computation techniques to detect these bouquet structures.

For the second stage of this project, I propose an alternative centrality measure for the professional networks using topological data analysis. We aim to compare the centrality measures proposed in this project against the career success of relevant Members of Parliament.

I also include a published paper in positron physics where we computed the ground state energy of a quasi-free positron in noble gases. This was completed before a change in supervision. Show more