Benjamin Burton

Benjamin Burton's research interests include computational geometry and topology, combinatorics, and information security. He also maintains an active role in gifted-and-talented programmes for secondary school students. Benjamin Burton's research involves a blend of techniques from pure mathematics and computer science. His main interest is in computational geometry and topology in three and four dimensions, looking at problems such as how a computer can recognise whether a loop of string is knotted, or how it can identify large-scale geometric structures in a three-dimensional space. He is the primary author of the open source software package Regina, which implements state-of-the-art algorithms in this field. His multi-disciplinary background includes a PhD in geometry and topology, an honours degree in combinatorics, research experience in information security, and three years as a research analyst in the finance industry. He has worked at several universities in Australia and overseas. He maintains a strong interest in enrichment programmes for gifted and talented high school students, including the Mathematics and Informatics Olympiads and the National Mathematics Summer School. From 1999 until 2008 he directed the Australian training programme for the International Olympiad in Informatics (IOI), and from 2009 to 2014 he holds a seat on the international IOI Scientific Committee. Benjamin is an active member of the UQ Ally Network, an award-winning program that supports and celebrates diversity of sexuality, gender and sex at UQ and in the broader community. Computational geometry and topology, combinatorics, and information security

[2026] Small triangulations of 4-manifolds and the 4-manifold census. Discrete and Computational Geometry. doi: 10.1007/s00454-026-00818-w [2026] Remarks on the Montesinos-Nakanishi 3-move conjecture. MATRIX Book Series. (pp. 401-410) Cham, Switzerland: Springer Cham. doi: 10.1007/978-3-032-16202-1_17 [2026] Connecting 3-manifold triangulations with unimodal sequences of elementary moves. Discrete and Computational Geometry, 75 (4), 1306-1330. doi: 10.1007/s00454-025-00735-4 [2025] Computing closed essential surfaces in 3-manifolds. Journal of Applied and Computational Topology, 9 (3) 18, 1-42. doi: 10.1007/s41468-025-00208-w [2025] Small triangulations of 4-manifolds and the 4-manifold census. 41st International Symposium on Computational Geometry (SoCG 2025), Kanazawa, Japan, 23-27 June