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.
We have a preprint (see arXiv:2403.11659), which also appears in the conference proceedings for the 40th International Symposium on Computational Geometry (see LIPIcs, Volume 293).
The code for it is available on Github.
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.
In October 2022, I spoke at (GT)^2 - Graduate Talks in Geometry and Topology on my work on Heegaard genus computation.
I spoke at the 40th International Symposium on Computational Geometry (SoCG 2024). My slides are available here.
I presented a similar talk at 'Hodgsonfest' (Geometry and Topology in Low Dimensions), and at the Joint Meeting of the NZMS, AustMS and AMS.
I spoke at the Australian Geometric Topology Webinar (AGTW) on 'Numerically investigating the space writhe and rope length of knots'
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)
Finn Thompson, Maria Maalouf and Alexander R. Klotz. The space writhes and signatures of polymer knots. arXiv:2501.02139
Alexander R. Klotz, Finn Thompson. Ropelength-minimizing concentric helices and non-alternating torus knots. arXiv:2501.02139