About

I am currently a Postdoctoral Research Associate at the Mathematical Institute, University of Oxford.

I completed my PhD 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 (last updated: 2025-10-03).

Papers

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

  2. Small Triangulations of 4-Manifolds and the 4-Manifold Census (with Ben Burton and Jonathan Spreer), 2025, in 41st International Symposium on Computational Geometry (SoCG 2025).
    arXiv version: 2412.04768

  3. Algorithms in 4-manifold topology (with M. Kegel, M. Powell, et al.), 2024, to appear in Algebraic and Geometric Topology.
    arXiv : 2411.08775

  4. Practical Software for Triangulating and Simplifying 4-Manifolds, 2024, Journal of Computational Geometry 16 (2):109–144.
    arXiv : 2402.15087
    Conference version : here.

  5. 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.

This page was last updated: 2025-10-05