Skip to menu Skip to content Skip to footer
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

41 - 60 of 76 works

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

Optimising a nonlinear utility function in multi-objective integer programming

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

A tree traversal algorithm for decision problems in knot theory and 3-manifold topology

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.

Computationally proving triangulated 4-manifolds to be diffeomorphic

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

Parameterized complexity of discrete morse theory

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

Computing closed essential surfaces in knot complements

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

Computing closed essential surfaces in knot complements

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

Locating regions in a sequence under density constraints

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

A new approach to crushing 3-manifold triangulations

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

Computing the crosscap number of a knot using integer programming and normal surfaces

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

Computational topology and normal surfaces: theoretical and experimental complexity bounds

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

Complementary vertices and adjacency testing in polytopes

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

Pachner moves, generic complexity, and randomising 3-manifold triangulations

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

Triangulating a Cappell-Shaneson knot complement

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

Searching a bitstream in linear time for the longest substring of any given density

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

Maximal admissible faces and asymptotic bounds for the normal surface solution space

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

Detecting genus in vertex links for the fast enumeration of 3-manifold triangulations

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

A tree traversal algorithm for decision problems in knot theory and 3-manifold topology

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

The Pachner graph and the simplification of 3-sphere triangulations

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

The complexity of the normal surface solution space

2010

Journal Article

Optimizing the double description method for normal surface enumeration

Burton, Benjamin A. (2010). Optimizing the double description method for normal surface enumeration. Mathematics of Computation, 79 (269), 453-484. doi: 10.1090/S0025-5718-09-02282-0

Optimizing the double description method for normal surface enumeration

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

Before you email them, read our advice on how to contact a supervisor.

Supervision history

Current supervision

  • Doctor Philosophy

    Computational complexity of topological problems

    Principal Advisor

    Other advisors: Associate Professor Barbara Maenhaut

  • Doctor Philosophy

    Computational 4-manifold topology

    Principal Advisor

    Other advisors: Dr Ramiro Lafuente

  • 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

Need help?

For help with finding experts, story ideas and media enquiries, contact our Media team:

communications@uq.edu.au