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
Featured
2013
Conference Publication
The complexity of detecting taut angle structures on triangulations
Burton, Benjamin and Spreer, Jonathan (2013). The complexity of detecting taut angle structures on triangulations. 24th ACM-SIAM Symposium on Discrete Algorithms (SODA 2013), New Orleans, United States, 6-9 January 2013. Philadelphia, United States: Society for Industrial and Applied Mathematics. doi: 10.1137/1.9781611973105.13
Featured
2013
Book Chapter
Computational topology with regina: algorithms, heuristics and implementations
Burton, Benjamin A. (2013). Computational topology with regina: algorithms, heuristics and implementations. Geometry and topology down under: a conference in honour of Hyam Rubinstein. (pp. 195-224) edited by Craig D. Hodgson, William H. Jaco, Martin G. Scharlemann and Stephan Tillmann. Providence, RI, United States: American Mathematical Society. doi: 10.1090/conm/597/11877
Featured
2012
Journal Article
The Weber-Seifert dodecahedral space is non-Haken
Burton, Benjamin A., Rubinstein, J. Hyam and Tillmann, Stephan (2012). The Weber-Seifert dodecahedral space is non-Haken. Transactions of the American Mathematical Society, 364 (2), 911-932. doi: 10.1090/S0002-9947-2011-05419-X
Featured
2010
Journal Article
A mathematician reflecting on the International Olympiad in Informatics
Burton, Benjamin A. (2010). A mathematician reflecting on the International Olympiad in Informatics. Australian Mathematical Society Gazette, 37 (1), 15-21.
2024
Journal Article
Arc diagrams on 3-manifold spines
Brand, Jack, Burton, Benjamin A., Dancso, Zsuzsanna, He, Alexander, Jackson, Adele and Licata, Joan (2024). Arc diagrams on 3-manifold spines. Discrete and Computational Geometry, 71 (4), 1190-1209. doi: 10.1007/s00454-023-00539-4
2023
Conference Publication
Finding large counterexamples by selectively exploring the Pachner graph
Burton, Benjamin A. and He, Alexander (2023). Finding large counterexamples by selectively exploring the Pachner graph. Symposium on Computational Geometry (SoCG), Dallas, TX, United States, 12-15 June 2023. Wadern, Germany: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik. doi: 10.4230/LIPIcs.SoCG.2023.21
2023
Journal Article
Hard Diagrams of the Unknot
Burton, Benjamin A., Chang, Hsien-Chih, Löffler, Maarten, Maria, Clément, de Mesmay, Arnaud, Schleimer, Saul, Sedgwick, Eric and Spreer, Jonathan (2023). Hard Diagrams of the Unknot. Experimental Mathematics, 33 (3), 1-19. doi: 10.1080/10586458.2022.2161676
2022
Journal Article
Flip graphs of stacked and flag triangulations of the 2-sphere
Burton, Benjamin A., Datta, Basudeb and Spreer, Jonathan (2022). Flip graphs of stacked and flag triangulations of the 2-sphere. Electronic Journal of Combinatorics, 29 (2) P2.6. doi: 10.37236/10292
2022
Journal Article
Foreword
Burton, Benjamin (2022). Foreword. Olympiads in Informatics, 16, 1-2. doi: 10.15388/ioi.2022.00
2021
Journal Article
On the hardness of finding normal surfaces
Burton, Benjamin A. and He, Alexander (2021). On the hardness of finding normal surfaces. Journal of Applied and Computational Topology, 5 (4), 583-619. doi: 10.1007/s41468-021-00076-0
2020
Conference Publication
The next 350 million knots
Burton, Benjamin A. (2020). The next 350 million knots. 36th International Symposium on Computational Geometry (SoCG 2020), Zürich, Switzerland, 23-26 June 2020. Wadern, Germany: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH. doi: 10.4230/LIPIcs.SoCG.2020.25
2020
Conference Publication
Knot Diagrams of Treewidth Two
Bodlaender, Hans L., Burton, Benjamin, Fomin, Fedor V. and Grigoriev, Alexander (2020). Knot Diagrams of Treewidth Two. 46th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2020), Online, 24–26 June 2020. Heidelberg, Germany: Springer. doi: 10.1007/978-3-030-60440-0_7
2020
Journal Article
Embeddings of 3-Manifolds in S4 from the Point of View of the 11-Tetrahedron Census
Budney, Ryan and Burton, Benjamin A. (2020). Embeddings of 3-Manifolds in S4 from the Point of View of the 11-Tetrahedron Census. Experimental Mathematics, 31 (3), 1-26. doi: 10.1080/10586458.2020.1740836
2019
Other Outputs
Tabulation of knots and 3-manifolds
Burton, Benjamin (2019). Tabulation of knots and 3-manifolds. The University of Queensland. (Dataset) doi: 10.48610/3bb4c69
2019
Journal Article
The parameterized complexity of finding a 2-sphere in a simplicial complex
Burton, Benjamin, Cabello, Sergio, Kratsch, Stefan and Pettersson, William (2019). The parameterized complexity of finding a 2-sphere in a simplicial complex. SIAM Journal on Discrete Mathematics, 33 (4), 2092-2110. doi: 10.1137/18M1168704
2018
Journal Article
Algorithms and complexity for Turaev–Viro invariants
Burton, Benjamin A., Maria, Clément and Spreer, Jonathan (2018). Algorithms and complexity for Turaev–Viro invariants. Journal of Applied and Computational Topology, 2 (1-2), 33-53. doi: 10.1007/s41468-018-0016-2
2018
Conference Publication
The HOMFLY-PT polynomial is fixed-parameter tractable
Burton, Benjamin A. (2018). The HOMFLY-PT polynomial is fixed-parameter tractable. 34th International Symposium on Computational Geometry, SoCG 2018, Budapest, Hungary, 11-14 June 2018. Wadern, Germany: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. doi: 10.4230/LIPIcs.SoCG.2018.18
2017
Conference Publication
Computing optimal homotopies over a spiked plane with polygonal boundary
Burton, Benjamin, Chambers, Erin, Van Kreveld, Marc, Meulemans, Wouter, Ophelders, Tim and Speckmann, Bettina (2017). Computing optimal homotopies over a spiked plane with polygonal boundary. 25th European Symposium on Algorithms, ESA 2017, Vienna, Austria, 4-6 September 2017. Wadern, Germany: Schloss Dagstuhl - Leibniz-Zentrum fur Informatik GmbH. doi: 10.4230/LIPIcs.ESA.2017.23
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
Funding
Supervision
Availability
- Professor Benjamin Burton is:
- Available for supervision
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Supervision history
Current supervision
-
Doctor Philosophy
Computational 4-manifold topology
Principal Advisor
Other advisors: Dr Ramiro Lafuente
-
Doctor Philosophy
Computational complexity of topological problems
Principal Advisor
Other advisors: Associate Professor Barbara Maenhaut
-
Master Philosophy
Practical computation of topological invariants
Principal Advisor
-
Doctor Philosophy
Applying Operations Research techniques to Pure Mathematics problems
Associate Advisor
Other advisors: Dr Michael Forbes
Completed supervision
-
2016
Doctor Philosophy
Graph Algorithms and Network Motifs: Tools for Text Exploration
Principal Advisor
Other advisors: Professor Lorraine Mazerolle
-
-
2016
Doctor Philosophy
Latin Squares and Related Structures
Associate Advisor
Other advisors: Professor Diane Donovan
-
2014
Doctor Philosophy
Computational Graph Theory
Associate Advisor
Other advisors: Professor Darryn Bryant, Associate Professor Barbara Maenhaut
-
2013
Doctor Philosophy
Orthogonal Arrays; Enumeration and Applications
Associate Advisor
Other advisors: Professor Diane Donovan
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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