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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

1 - 20 of 76 works

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

The complexity of detecting taut angle structures on triangulations

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

Computational topology with regina: algorithms, heuristics and implementations

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

The Weber-Seifert dodecahedral space is non-Haken

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.

A mathematician reflecting on the International Olympiad in Informatics

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

Arc diagrams on 3-manifold spines

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

Finding large counterexamples by selectively exploring the Pachner graph

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

Hard Diagrams of the Unknot

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

Flip graphs of stacked and flag triangulations of the 2-sphere

2022

Journal Article

Foreword

Burton, Benjamin (2022). Foreword. Olympiads in Informatics, 16, 1-2. doi: 10.15388/ioi.2022.00

Foreword

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

On the hardness of finding normal surfaces

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

The next 350 million knots

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

Embeddings of 3-Manifolds in S4 from the Point of View of the 11-Tetrahedron Census

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

Knot Diagrams of Treewidth Two

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

Tabulation of knots and 3-manifolds

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

The parameterized complexity of finding a 2-sphere in a simplicial complex

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

Algorithms and complexity for Turaev–Viro invariants

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

The HOMFLY-PT polynomial is fixed-parameter tractable

2017

Conference Publication

The parameterized complexity of finding a 2-sphere in a simplicial complex

Burton, Benjamin, Cabello, Sergio, Kratsch, Stefan and Pettersson, William (2017). The parameterized complexity of finding a 2-sphere in a simplicial complex. 34th Symposium on Theoretical Aspects of Computer Science, STACS 2017, Hannover, Germany, 8 - 11 March 2017. Wadern, Germany: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH. doi: 10.4230/LIPIcs.STACS.2017.18

The parameterized complexity of finding a 2-sphere in a simplicial complex

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

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

Randomness testing and comparison of classical and quantum bit generators

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 complexity of topological problems

    Principal Advisor

    Other advisors: Associate Professor Barbara Maenhaut

  • Master Philosophy

    Practical computation of topological invariants

    Principal Advisor

  • Doctor Philosophy

    Computational 4-manifold topology

    Principal Advisor

    Other advisors: Dr Ramiro Lafuente

  • 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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