
Overview
Background
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.
Availability
- Professor Benjamin Burton is:
- Available for supervision
- Media expert
Fields of research
Qualifications
- Bachelor (Honours) of Science, The University of Queensland
- Doctor of Philosophy, University of Melbourne
Works
Search Professor Benjamin Burton’s works on UQ eSpace
2017
Conference Publication
Randomness testing and comparison of classical and quantum bit generators
Boztas, Serdar and Burton, Benjamin A. (2017). Randomness testing and comparison of classical and quantum bit generators. 2017 IEEE Symposium on Computers and Communications (ISCC), , Heraklion, Greece, 3-6 July 2017. Piscataway, NJ United States: Institute of Electrical and Electronics Engineers . doi: 10.1109/ISCC.2017.8024660
2017
Conference Publication
Finding Non-orientable Surfaces in 3-Manifolds
Burton, Benjamin A., de Mesmay, Arnaud and Wagner, Uli (2017). Finding Non-orientable Surfaces in 3-Manifolds. 32nd Annual ACM International Symposium on Computational Geometry (SoCG), Boston Ma, Jun 14-17, 2016. New York, NY United States: Springer New York. doi: 10.1007/s00454-017-9900-0
2016
Journal Article
Courcelle's theorem for triangulations
Burton, Benjamin A. and Downey, Rodney G. (2016). Courcelle's theorem for triangulations. Journal of Combinatorial Theory. Series A, 146, 264-294. doi: 10.1016/j.jcta.2016.10.001
2016
Journal Article
A construction principle for tight and minimal triangulations of manifolds
Burton, Benjamin A., Datta, Basudeb, Singh, Nitin and Spreer, Jonathan (2016). A construction principle for tight and minimal triangulations of manifolds. Experimental Mathematics, 27 (1), 22-36. doi: 10.1080/10586458.2016.1212747
2016
Journal Article
Combinatorial Seifert fibred spaces with transitive cyclic automorphism group
Burton, Benjamin and Spreer, Jonathan (2016). Combinatorial Seifert fibred spaces with transitive cyclic automorphism group. Israel Journal of Mathematics, 214 (2), 741-784. doi: 10.1007/s11856-016-1330-9
2016
Journal Article
On the complexity of immersed normal surfaces
Burton, Benjamin A., de Verdière, Éric Colin and de Mesmay, Arnaud (2016). On the complexity of immersed normal surfaces. Geometry and Topology, 20 (2), 1061-1083. doi: 10.2140/gt.2016.20.1061
2016
Journal Article
Parameterized complexity of discrete Morse theory
Burton, Benjamin A., Lewiner, Thomas, Paixao, Joao and Spreer, Jonathan (2016). Parameterized complexity of discrete Morse theory. ACM Transactions On Mathematical Software, 42 (1) 2738034, 6:1-6:24. doi: 10.1145/2738034
2016
Conference Publication
Finding non-orientable surfaces in 3-manifolds
Burton, Benjamin A., de Mesmay, Arnaud and Wagner, Uli (2016). Finding non-orientable surfaces in 3-manifolds. International Symposium on Computational Geometry, Boston, MA, United States, 14-17 June 2016. Wadern, Germany: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik. doi: 10.4230/LIPIcs.SoCG.2016.24
2016
Journal Article
2-manifold recognition is in logspace
Burton, Benjamin A., Elder, Murray, Kalka, Arkadius and Tillmann, Stephan (2016). 2-manifold recognition is in logspace. Journal of Computational Geometry, 7 (1), 70-85.
2016
Conference Publication
Efficient algorithms to decide tightness
Bagchi, Bhaskar, Datta, Basudeb, Burton, Benjamin A., Singh, Nitin and Spreer, Jonathan (2016). Efficient algorithms to decide tightness. International Symposium on Computational Geometry, Boston, MA, United States, 14-18 June 2016. Wadern, Germany: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik. doi: 10.4230/LIPIcs.SoCG.2016.12
2015
Journal Article
Separation index of graphs and stacked 2-spheres
Burton, Benjamin, Datta, Basudeb, Singh, Nitin and Spreer, Jonathan (2015). Separation index of graphs and stacked 2-spheres. Journal of Combinatorial Theory. Series A, 136, 184-197. doi: 10.1016/j.jcta.2015.07.001
2015
Conference Publication
Algorithms and complexity for Turaev-Viro invariants
Burton, Benjamin A., Maria, Clément and Spreer, Jonathan (2015). Algorithms and complexity for Turaev-Viro invariants. International Colloquium on Automata, Languages, and Programming, Kyoto, Japan, 6-10 June 2015. Heidelberg, Germany: Springer. doi: 10.1007/978-3-662-47672-7_23
2015
Conference Publication
Tabulation of 3-manifolds of lengths up to 10
Kawauchi, Akio, Tayama, Ikuo and Burton, Benjamin (2015). Tabulation of 3-manifolds of lengths up to 10. International Conference on Topology and Geometry 2013, joint with the Sixth Japan-Mexico Topology Symposium, Matsue, Japan, September 2-6, 2013. Amsterdam, Netherlands: Elsevier BV. doi: 10.1016/j.topol.2015.05.036
2015
Conference Publication
An edge-based framework for enumerating 3-manifold triangulations
Burton, Benjamin A. and Pettersson, William (2015). An edge-based framework for enumerating 3-manifold triangulations. International Symposium on Computational Geometry, Eindhoven, Netherlands, 22-25 June 2015. Wadern, Germany: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. doi: 10.4230/LIPIcs.SOCG.2015.270
2014
Journal Article
A new approach to crushing 3-manifold triangulations
Burton, Benjamin A. (2014). A new approach to crushing 3-manifold triangulations. Discrete and Computational Geometry, 52 (1), 116-139. doi: 10.1007/s00454-014-9572-y
2014
Journal Article
A duplicate pair in the SnapPea census
Burton, Benjamin A. (2014). A duplicate pair in the SnapPea census. Experimental Mathematics, 23 (2), 170-173. doi: 10.1080/10586458.2014.886535
2014
Conference Publication
Courcelle's theorem for triangulations
Burton, Benjamin A. (2014). Courcelle's theorem for triangulations. Workshop on Triangulations in Geometry and Topology. SoCG 2014: Computational Geometry Week 2014. The 30th Annual Symposium on Computational Geometry, Kyoto, Japan, 8-11 June, 2014. Ithaca, NY, USA: Cornell University Library.
2014
Conference Publication
Enumerating fundamental normal surfaces: algorithms, experiments and invariants
Burton, Benjamin A. (2014). Enumerating fundamental normal surfaces: algorithms, experiments and invariants. 16th Workshop on Algorithm Engineering and Experiments (ALENEX14), Portland, United States, 5 January 2014. Philadelphia, United States: Society for Industrial and Applied Mathematics (SIAM). doi: 10.1137/1.9781611973198.11
2014
Journal Article
Multi-objective integer programming: an improved recursive algorithm
Ozlen, Melih, Burton, Benjamin A. and MacRae, Cameron A. G. (2014). Multi-objective integer programming: an improved recursive algorithm. Journal of Optimization Theory and Applications, 160 (2), 470-482. doi: 10.1007/s10957-013-0364-y
2014
Conference Publication
Fixed parameter tractable algorithms in combinatorial topology
Burton, Benjamin A. and Pettersson, William (2014). Fixed parameter tractable algorithms in combinatorial topology. 20th International Computing and Combinatorics Conference, COCOON 2014, Atlanta, GA United States, 2 - 6 August 2014. Heidelberg, Germany: Springer. doi: 10.1007/978-3-319-08783-2_26
Funding
Supervision
Availability
- Professor Benjamin Burton is:
- Available for supervision
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Supervision history
Current supervision
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Doctor Philosophy
Efficient algorithms in three-dimensional topology
Principal Advisor
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Doctor Philosophy
Applying Operations Research techniques to Pure Mathematics problems
Associate Advisor
Other advisors: Dr Michael Forbes
Completed supervision
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2025
Doctor Philosophy
A computational approach to 4-manifold topology
Principal Advisor
Other advisors: Associate Professor Ramiro Lafuente
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2024
Doctor Philosophy
Combinatorial transformations in 3-manifold topology
Principal Advisor
Other advisors: Associate Professor Barbara Maenhaut
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2016
Doctor Philosophy
Graph Algorithms and Network Motifs: Tools for Text Exploration
Principal Advisor
Other advisors: Professor Lorraine Mazerolle
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-
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2014
Doctor Philosophy
Computational Graph Theory
Associate Advisor
Other advisors: Professor Darryn Bryant, Associate Professor Barbara Maenhaut
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Media
Enquiries
Contact Professor Benjamin Burton directly for media enquiries about:
- Algorithms
- Competitions - computer programming
- Competitions - mathematics
- Computation
- Computer programming competitions
- Cryptography
- Geometry
- International Mathematical Olympiad
- International Olympiad in Informatics
- Knot theory
- Mathematics competitions
- Olympics
- Science olympiads
- Topology
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