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Professor Benjamin Burton
Professor

Benjamin Burton

Email: 
Phone: 
+61 7 336 51164

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

76 works between 2004 and 2024

21 - 40 of 76 works

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

Computing optimal homotopies over a spiked plane with polygonal boundary

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

Courcelle's theorem for triangulations

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

A construction principle for tight and minimal triangulations of manifolds

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

Combinatorial Seifert fibred spaces with transitive cyclic automorphism group

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

On the complexity of immersed normal surfaces

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

Parameterized complexity of discrete Morse theory

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.

2-manifold recognition is in logspace

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

Efficient algorithms to decide tightness

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

Finding non-orientable surfaces in 3-manifolds

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

Separation index of graphs and stacked 2-spheres

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

An edge-based framework for enumerating 3-manifold triangulations

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

Algorithms and complexity for Turaev-Viro invariants

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

Tabulation of 3-manifolds of lengths up to 10

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

A new approach to crushing 3-manifold triangulations

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

A duplicate pair in the SnapPea census

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

Multi-objective integer programming: an improved recursive algorithm

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

Fixed parameter tractable algorithms in combinatorial topology

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.

Courcelle's theorem for triangulations

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

Enumerating fundamental normal surfaces: algorithms, experiments and invariants

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

A new approach to crushing 3-manifold triangulations

Funding

Past funding

  • 2015 - 2023
    Tractable topological computing: Escaping the hardness trap
    ARC Discovery Projects
    Open grant
  • 2014 - 2017
    Building triangulations for fast topological computing
    Department of Innovation, Industry, Science and Research - Australia-India Strategic Research Fund
    Open grant
  • 2014 - 2017
    Unlocking the potential for linear and discrete optimisation in knot theory and computational topology
    ARC Discovery Projects
    Open grant
  • 2013
    Australia Japan Emerging Research Leaders Exchange Program (ERLEP) 2012
    Department of Innovation, Industry, Science and Research
    Open grant
  • 2012 - 2013
    Algorithmic methods in combinatorial topology
    Go8 Australia - Germany Joint Research Co-operation Scheme
    Open grant
  • 2011 - 2012
    Complexity in topology: is unknot recognition as difficult as it seems?
    UQ Early Career Researcher
    Open grant
  • 2011 - 2013
    Generic complexity in computational topology: Breaking through the bottlenecks
    ARC Discovery Projects
    Open grant
  • 2011
    New-generation parallel-computing cluster for the mathematical and physical sciences
    UQ Major Equipment and Infrastructure
    Open grant
  • 2011
    ResTeach 2011 0.1 FTE School of mathematics and Physics
    UQ ResTeach
    Open grant
  • 2011
    UQ Travel Awards Category 1 - Mr Mathias Hiron
    UQ Travel Grants Scheme
    Open grant
  • 2010 - 2011
    Fast algorithms for string processing in cryptography and bioinformatics
    UQ New Staff Research Start-Up Fund
    Open grant
  • 2010 - 2015
    Algorithms and computation in four-dimensional topology
    ARC Discovery Projects
    Open grant

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

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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