Research

Papers

Benjamin A. Burton and Finn Thompson. Effective Computation of the Heegaard Genus of 3-Manifolds. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024). doi.org/10.4230/LIPIcs.SoCG.2024.30
Finn Thompson, Maria Maalouf and Alexander R. Klotz. The space writhes and signatures of polymer knots. Eur. Phys. J. B 98, 89 (2025). doi.org/10.1140/epjb/s10051-025-00942-1
Alexander R. Klotz and Finn Thompson. Ropelength-minimizing concentric helices and non-alternating torus knots. Proc. R. Soc. A. 481 (2025). doi.org/10.1098/rspa.2025.0319
Benjamin A. Burton and Finn Thompson. Effective Computation of the Heegaard Genus of 3-Manifolds. Journal of Computational Geometry 16 (2):207-236. doi.org/10.20382/jocg.v16i2a7 (Extended version of the original publication, in the special issue of JoCG Special Issue of Selected Papers from SoCG 2024)

Talks

During my undergraduate study at UQ, I frequently spoke at the informal analysis seminar, and organised/co-organised it from semester 2 2019 until semester 1 2021.
(October 2022) On Heegaard genus computation, at (GT)^2 - Graduate Talks in Geometry and Topology.
(June 2024) On Effective Computation of the Heegaard Genus of 3-Manifolds, at 40th International Symposium on Computational Geometry (SoCG 2024). My slides are available here.
(November 2024) On Heegaard genus computation, at 'Hodgsonfest' (Geometry and Topology in Low Dimensions)
(December 2024) ... and at the Joint Meeting of the NZMS, AustMS and AMS.
(March 2025) Numerically investigating the space writhe and rope length of knots, at Australian Geometric Topology Webinar (AGTW)
(October 2025) Why Knot use Grid Diagrams? at The University of Queensland School of Mathematics and Physics Graduate Student Seminar
(December 2025) Numerically investigating the space writhe and rope length of knots at AustMS 2025.

Conferences/workshops/etc

You may have seen me at:

Heegaard genus

I have been working with Ben Burton on implementing an algorithm to determine the Heegaard genus of a triangulation of a 3-manifold by finding a splitting.

Our paper appears in the conference proceedings for the 40th International Symposium on Computational Geometry (see LIPIcs, Volume 293), and in the related special issue of the Journal of Computational Geometry (see JoCG, Volume 16(1))

The code for it is available on Github.

3D numeric knot invariants

I'm interested in physical constraints on knots relating to invariants — such as ropelength, and writhe.