About

I am a PhD student at the University of Queensland (UQ), Australia. My research is in computational topology, specifically, I am interested in using computational techniques to study standard and exotic 4-manifolds. My CV.

Papers

  1. Observations on the Structure of Small 4-Manifold Triangulations, In Preparation.

  2. Algorithms in 4-manifold topology (with M. Kegel, M. Powell, et al.)
    arXiv : 2411.08775

  3. Practical Software for Triangulating and Simplifying 4-Manifolds, 2024, in The 40th International Symposium on Computational Geometry (SoCG 2024).
    arXiv : 2402.15087

  4. Triangulations of Exotic 4-Manifolds, 2021, Extended Abstract for the Young Researchers Forum — 37th International Symposium on Computational Geometry (SoCG 2021).

Software

A large part of my research involves developing software for use in computational topology. Katie and USDS are the two primary pieces I have written as part of my “computational approach to 4-manifold topology” project.

Katie is software for building triangulations and coloured graph representations of 4-manifolds from Kirby diagrams.
USDS is a utility which implements my “Up-Side-Down Simplification” heuristic for 4-manifold triangulations.

Mathematical details can be found in the papers linked above.
The source code for both programs, as well as other pieces of software, scripts, examples, and documentation, is available here.