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Professor Benjamin Burton

Professor

Mathematics
Faculty of Science
bab@maths.uq.edu.au
+61 7 336 51164

Overview

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.

Qualifications

  • PhD, University of Melbourne
  • Bachelor of Science with Honours First Class, The University of Queensland

Publications

  • 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

  • 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

  • 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

  • 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.

View all Publications

Grants

View all Grants

Supervision

  • Practical computation of topological invariants

    Master Philosophy

  • Computational 4-manifold topology

    Doctor Philosophy

  • Computational complexity of topological problems

    Doctor Philosophy

View all Supervision

Publications

Featured Publications

  • 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

  • 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 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

  • 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.

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

Journal Article

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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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.

  • 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

  • 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

  • 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 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 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

  • 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.

  • 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

    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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • Encouraging algorithmic thinking without a computer

    Burton, Benjamin A. (2010). Encouraging algorithmic thinking without a computer. Lithuania: Institute of Mathematics and Informatics.

  • Get involved! The IOI workshop 2010, its goals and results

    Pohl, Wolfgang, Burton, Benjamin A., Dagiene, Valentina, Fakcharoenphol, Jittat, Forišek, Michal, Hiron, Mathias, Opmanis, Martiņš, Skupas, Bronius and Van Der Vegt, Willem (2010). Get involved! The IOI workshop 2010, its goals and results. Vilnius University.

  • 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

  • Informatics Olympiads: Challenges in programming and algorithm design

    Burton, Benjamin A. (2008). Informatics Olympiads: Challenges in programming and algorithm design. Thirty-First Australasian Computer Science Conference (ACSC 2008), Wollongong, NSW, Australia, 22-25 Jan 2008. Sydney, Australia: Australian Computer Society (ACS).

  • Secure group communication with distributed generation of private keys for ad-hoc networks

    Sundaram, Shrikant, Bertok, Peter and Burton, Benjamin (2005). Secure group communication with distributed generation of private keys for ad-hoc networks. IFIP TC11 20th IFIP International Information Security Conference, Chiba, Japan, 3 May- 1 Jun 2005. New York, USA: Springer. doi: 10.1007/0-387-25660-1_31

Other Outputs

Grants (Administered at UQ)

PhD and MPhil Supervision

Current Supervision

  • Practical computation of topological invariants

    Master Philosophy — Principal Advisor

  • Computational 4-manifold topology

    Doctor Philosophy — Principal Advisor

    Other advisors:

  • Computational complexity of topological problems

    Doctor Philosophy — Principal Advisor

    Other advisors:

Completed Supervision

This staff member is a UQ Expert for media in the following fields:

Geometry, Topology, Algorithms, Computation, Mathematics competitions, Competitions - mathematics, Computer programming competitions, Competitions - computer programming, Knot theory, Cryptography, Science olympiads, Olympics, International Mathematical Olympiad, International Olympiad in Informatics

They are happy to lend their expertise to your articles or broadcasts and share their research discoveries and insights with the community via media channels.

For additional assistance with story ideas, general advice and information or help with seeking further experts, please email the UQ Media Team or telephone (07) 3365 1120.

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