
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
2013
Conference Publication
A new approach to crushing 3-manifold triangulations
Burton, Benjamin A. (2013). A new approach to crushing 3-manifold triangulations. SoCG '13: Symposium on Computational Geometry 2013, Rio de Janeiro, Brazil, 17 - 20 June 2013. New York, NY United States: Association for Computing Machinery. doi: 10.1145/2493132.2462409
2013
Journal Article
Optimising a nonlinear utility function in multi-objective integer programming
Ozlen, Melih, Azizoglu, Meral and Burton, Benjamin A. (2013). Optimising a nonlinear utility function in multi-objective integer programming. Journal of Global Optimization, 56 (1), 93-102. doi: 10.1007/s10898-012-9921-4
2013
Conference Publication
A tree traversal algorithm for decision problems in knot theory and 3-manifold topology
Burton, Benjamin A. and Ozlen, Melih (2013). A tree traversal algorithm for decision problems in knot theory and 3-manifold topology. Secaucus, NJ, United States: Springer. doi: 10.1007/s00453-012-9645-3
2013
Conference Publication
Computationally proving triangulated 4-manifolds to be diffeomorphic
Burton, Benjamin and Spreer, Jonathan (2013). Computationally proving triangulated 4-manifolds to be diffeomorphic. 29th ACM Symposium on Computational Geometry,, Rio de Janeiro, Brazil, 17 - 20 June 2013.
2013
Conference Publication
Parameterized complexity of discrete morse theory
Burton, Benjamin A., Lewiner, Thomas, Paixao, Joao and Spreer, Jonathan (2013). Parameterized complexity of discrete morse theory. 29th Annual Symposium on Computational Geometry (SoCG 2013), Rio de Janeiro, Brazil, 17-20 June 2013. New York, NY, United States: Association for Computing Machinery Inc.. doi: 10.1145/2462356.2462391
2013
Conference Publication
Computing closed essential surfaces in knot complements
Burton, Benjamin A., Coward, Alexander and Tillmann, Stephan (2013). Computing closed essential surfaces in knot complements. SoCG '13: Symposium on Computational Geometry 2013, Rio de Janeiro, Brazil, 17 - 20 June 2013. New York, NY United States: Association for Computing Machinery. doi: 10.1145/2493132.2462380
2013
Conference Publication
Computing closed essential surfaces in knot complements
Burton, Benjamin A., Coward, Alexander and Tillmann, Stephen (2013). Computing closed essential surfaces in knot complements. 29th Annual Symposium on Computational Geometry (SoCG 2013), Rio de Janeiro, Brazil, 17-20 June 2013. New York, NY United States: Association for Computing Machinery Inc.. doi: 10.1145/2462356.2462380
2013
Journal Article
Locating regions in a sequence under density constraints
Burton, Benjamin A. and Hiron, Mathias (2013). Locating regions in a sequence under density constraints. SIAM Journal on Computing, 42 (3), 1201-1215. doi: 10.1137/110830605
2013
Conference Publication
A new approach to crushing 3-manifold triangulations
Burton, Benjamin A. (2013). A new approach to crushing 3-manifold triangulations. 29th Annual Symposium on Computational Geometry (SoCG 2013), Rio de Janeiro, Brazil, 17-20 June 2013. New York, NY United States: Association for Computing Machinery Inc.. doi: 10.1145/2462356.2462409
2012
Journal Article
Computing the crosscap number of a knot using integer programming and normal surfaces
Burton, Benjamin A. and Ozlen, Melih (2012). Computing the crosscap number of a knot using integer programming and normal surfaces. ACM Transactions On Mathematical Software, 39 (1) 4, 4.1-4.18. doi: 10.1145/2382585.2382589
2012
Conference Publication
Complementary vertices and adjacency testing in polytopes
Burton, Benjamin A. (2012). Complementary vertices and adjacency testing in polytopes. 18th Annual International Computing and Combinatorics Conference (COCOON 2012), Sydney, Australia, 20-22 August 2012. Heidelberg, Germany: Springer. doi: 10.1007/978-3-642-32241-9_43
2012
Conference Publication
Computational topology and normal surfaces: theoretical and experimental complexity bounds
Burton, Benjamin, Paixao, Joao and Spreer, Jonathan (2012). Computational topology and normal surfaces: theoretical and experimental complexity bounds. Meeting on Algorithm Engineering and Experiments (ALENEX13), New Orleans, United States, 7 January 2013. Philadelphia, United States: Society for Industrial and Applied Mathematics. doi: 10.1137/1.9781611972931.7
2012
Journal Article
Pachner moves, generic complexity, and randomising 3-manifold triangulations
Burton, Benjamin A. (2012). Pachner moves, generic complexity, and randomising 3-manifold triangulations. Oberwolfach Reports, 9 (2), 1412-1414. doi: 10.4171/OWR/2012/24
2012
Journal Article
Triangulating a Cappell-Shaneson knot complement
Budney, Ryan, Burton, Benjamin A. and Hillman, Jonathan (2012). Triangulating a Cappell-Shaneson knot complement. Mathematical Research Letters, 19 (5), 1117-1126. doi: 10.4310/MRL.2012.v19.n5.a12
2011
Journal Article
Searching a bitstream in linear time for the longest substring of any given density
Burton, Benjamin A. (2011). Searching a bitstream in linear time for the longest substring of any given density. Algorithmica, 61 (3), 555-579. doi: 10.1007/s00453-010-9424-y
2011
Journal Article
Maximal admissible faces and asymptotic bounds for the normal surface solution space
Burton, Benjamin A. (2011). Maximal admissible faces and asymptotic bounds for the normal surface solution space. Journal of Combinatorial Theory: Series A, 118 (4), 1410-1435. doi: 10.1016/j.jcta.2010.12.011
2011
Conference Publication
Detecting genus in vertex links for the fast enumeration of 3-manifold triangulations
Burton, Benjamin A. (2011). Detecting genus in vertex links for the fast enumeration of 3-manifold triangulations. 36th International Symposium on Symbolic and Algebraic Computation [ISSAC], San Jose, CA, United States, 8-11 June 2011. New York, NY, United States: ACM Press. doi: 10.1145/1993886.1993901
2011
Conference Publication
A tree traversal algorithm for decision problems in knot theory and 3-manifold topology
Burton, Benjamin A. and Ozlen, Melih (2011). A tree traversal algorithm for decision problems in knot theory and 3-manifold topology. 27th Annual Symposium on Computational Geometry (SoCG 2011), Paris, France, 13-15 June 2011. New York, NY, United States: ACM Press. doi: 10.1145/1998196.1998219
2011
Conference Publication
The Pachner graph and the simplification of 3-sphere triangulations
Burton, Benjamin A. (2011). The Pachner graph and the simplification of 3-sphere triangulations. 27th ACM Symposium on Computational Geometry [SoCG], Paris, France, 13-15 June 2011. New York, NY, U.S.A.: ACM. doi: 10.1145/1998196.1998220
2010
Conference Publication
The complexity of the normal surface solution space
Burton, Benjamin A. (2010). The complexity of the normal surface solution space. 26th ACM Symposium on Computational Geometry [SCG], Snowbird, Utah, U.S.A., 13-16 June 2010. New York , U.S.A.: ACM (Association for Computing Machinery) Press. doi: 10.1145/1810959.1810995
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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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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