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.

Qualifications

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

Publications

  • Burton, Benjamin A. (2013). Computational topology with regina: algorithms, heuristics and implementations. In Craig D. Hodgson, William H. Jaco, Martin G. Scharlemann and Stephan Tillmann (Ed.), Geometry and topology down under: a conference in honour of Hyam Rubinstein (pp. 195-224) Providence, RI, United States: American Mathematical Society. doi:10.1090/conm/597/11877

  • Burton, Benjamin and Spreer, Jonathan (2013). The complexity of detecting taut angle structures on triangulations. In: Sanjeev Khanna, Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms. 24th ACM-SIAM Symposium on Discrete Algorithms (SODA 2013), New Orleans, United States, (168-183). 6-9 January 2013.

  • 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

  • Burton, Benjamin A. (2010) A mathematician reflecting on the International Olympiad in Informatics. Australian Mathematical Society Gazette, 37 1: 15-21.

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Grants

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Supervision

View all Supervision

Publications

Featured Publications

  • Burton, Benjamin A. (2013). Computational topology with regina: algorithms, heuristics and implementations. In Craig D. Hodgson, William H. Jaco, Martin G. Scharlemann and Stephan Tillmann (Ed.), Geometry and topology down under: a conference in honour of Hyam Rubinstein (pp. 195-224) Providence, RI, United States: American Mathematical Society. doi:10.1090/conm/597/11877

  • Burton, Benjamin and Spreer, Jonathan (2013). The complexity of detecting taut angle structures on triangulations. In: Sanjeev Khanna, Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms. 24th ACM-SIAM Symposium on Discrete Algorithms (SODA 2013), New Orleans, United States, (168-183). 6-9 January 2013.

  • 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

  • Burton, Benjamin A. (2010) A mathematician reflecting on the International Olympiad in Informatics. Australian Mathematical Society Gazette, 37 1: 15-21.

Book Chapter

  • Burton, Benjamin A. (2013). Computational topology with regina: algorithms, heuristics and implementations. In Craig D. Hodgson, William H. Jaco, Martin G. Scharlemann and Stephan Tillmann (Ed.), Geometry and topology down under: a conference in honour of Hyam Rubinstein (pp. 195-224) Providence, RI, United States: American Mathematical Society. doi:10.1090/conm/597/11877

Journal Article

Conference Publication

  • Burton, Benjamin, Cabello, Sergio, Kratsch, Stefan and Pettersson, William (2017). The parameterized complexity of finding a 2-sphere in a simplicial complex. In: Heribert Vollmer and Brigitte Vallée, 34th Symposium on Theoretical Aspects of Computer Science, STACS 2017. 34th Symposium on Theoretical Aspects of Computer Science, STACS 2017, Hannover, Germany, (). 8 - 11 March 2017. doi:10.4230/LIPIcs.STACS.2017.18

  • Bagchi, Bhaskar, Datta, Basudeb, Burton, Benjamin A., Singh, Nitin and Spreer, Jonathan (2016). Efficient algorithms to decide tightness. In: Sandor Fekete and Anna Lubiw, 32nd International Symposium on Computational Geometry (SoCG 2016). International Symposium on Computational Geometry, Boston, MA, United States, (12:1-12:15). 14-18 June 2016. doi:10.4230/LIPIcs.SoCG.2016.12

  • Burton, Benjamin A., de Mesmay, Arnaud and Wagner, Uli (2016). Finding non-orientable surfaces in 3-manifolds. In: Sandor Fekete and Anna Lubiw, 32nd International Symposium on Computational Geometry (SoCG 2016). International Symposium on Computational Geometry, Boston, MA, United States, (24:1-24:15). 14-17 June 2016. doi:10.4230/LIPIcs.SoCG.2016.24

  • Burton, Benjamin A., Maria, Clément and Spreer, Jonathan (2015). Algorithms and complexity for Turaev-Viro invariants. In: Magnús M. Halldórsson, Kazuo Iwama, Naoki Kobayashi and Bettina Speckmann, Automata, Languages, and Programming: 42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6-10, 2015, Proceedings, Part 1. International Colloquium on Automata, Languages, and Programming, Kyoto, Japan, (281-293). 6-10 June 2015. doi:10.1007/978-3-662-47672-7_23

  • Burton, Benjamin A. and Pettersson, William (2015). An edge-based framework for enumerating 3-manifold triangulations. In: 31st International Symposium on Computational Geometry, SoCG 2015. International Symposium on Computational Geometry, Eindhoven, Netherlands, (270-284). 22-25 June 2015. doi:10.4230/LIPIcs.SOCG.2015.270

  • Kawauchi, Akio, Tayama, Ikuo and Burton, Benjamin (2015). Tabulation of 3-manifolds of lengths up to 10. In: International Conference on Topology and Geometry 2013, joint with the Sixth Japan-Mexico Topology Symposium, Matsue, Japan, (937-975). September 2-6, 2013. doi:10.1016/j.topol.2015.05.036

  • Burton, Benjamin A. (2014). Courcelle's theorem for triangulations. In: Jonathan Spreer and Uli Wagner, Collection of Abstracts of the Workshop on Triangulations in Geometry and Topology at CG Week 2014 in Kyoto. Workshop on Triangulations in Geometry and Topology. SoCG 2014: Computational Geometry Week 2014. The 30th Annual Symposium on Computational Geometry, Kyoto, Japan, (4-9). 8-11 June, 2014.

  • Burton, Benjamin A. (2014). Enumerating fundamental normal surfaces: algorithms, experiments and invariants. In: Ulrich Meyer and Catherine C. McGeoch, 2014 Proceedings of the Sixteenth Workshop on Algorithm Engineering and Experiments (ALENEX). 16th Workshop on Algorithm Engineering and Experiments (ALENEX14), Portland, United States, (112-124). 5 January 2014. doi:10.1137/1.9781611973198.11

  • Burton, Benjamin A. and Pettersson, William (2014). Fixed parameter tractable algorithms in combinatorial topology. In: Zhipeng Cai, Alex Zelikovsky and Anu Bourgeois, Computing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings. 20th International Computing and Combinatorics Conference, COCOON 2014, Atlanta, GA United States, (300-311). 2 - 6 August 2014. doi:10.1007/978-3-319-08783-2_26

  • Burton, Benjamin A. (2013). A new approach to crushing 3-manifold triangulations. In: Proceedings of the Annual Symposium on Computational Geometry. 29th Annual Symposium on Computational Geometry (SoCG 2013), Rio de Janeiro, Brazil, (415-424). 17-20 June 2013. doi:10.1145/2462356.2462409

  • Burton, Benjamin and Spreer, Jonathan (2013). Computationally proving triangulated 4-manifolds to be diffeomorphic. In: Young Researchers Forum, Collections of abstracts. 29th ACM Symposium on Computational Geometry,, Rio de Janeiro, Brazil, (15-16). 17 - 20 June 2013.

  • Burton, Benjamin A., Coward, Alexander and Tillmann, Stephen (2013). Computing closed essential surfaces in knot complements. In: Proceedings of the Annual Symposium on Computational Geometry. 29th Annual Symposium on Computational Geometry (SoCG 2013), Rio de Janeiro, Brazil, (405-414). 17-20 June 2013. doi:10.1145/2462356.2462380

  • Burton, Benjamin A., Lewiner, Thomas, Paixao, Joao and Spreer, Jonathan (2013). Parameterized complexity of discrete morse theory. In: Proceedings of the Annual Symposium on Computational Geometry. 29th Annual Symposium on Computational Geometry (SoCG 2013), Rio de Janeiro, Brazil, (127-136). 17-20 June 2013. doi:10.1145/2462356.2462391

  • Burton, Benjamin and Spreer, Jonathan (2013). The complexity of detecting taut angle structures on triangulations. In: Sanjeev Khanna, Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms. 24th ACM-SIAM Symposium on Discrete Algorithms (SODA 2013), New Orleans, United States, (168-183). 6-9 January 2013.

  • Burton, Benjamin A. (2012). Complementary vertices and adjacency testing in polytopes. In: Joachim Gudmundsson, Julián Mestre and Taso Viglas, Computing and Combinatorics: 18th Annual International Conference, COCOON 2012, proceedings. 18th Annual International Computing and Combinatorics Conference (COCOON 2012), Sydney, Australia, (507-518). 20-22 August 2012. doi:10.1007/978-3-642-32241-9_43

  • Burton, Benjamin, Paixao, Joao and Spreer, Jonathan (2012). Computational topology and normal surfaces: theoretical and experimental complexity bounds. In: Peter Sanders and Norbert Zeh, Proceedings of the Meeting on Algorithm Engineering & Experiments (ALENEX). Meeting on Algorithm Engineering and Experiments (ALENEX13), New Orleans, United States, (78-87). 7 January 2013.

  • Burton, Benjamin A. and Ozlen, Melih (2011). A tree traversal algorithm for decision problems in knot theory and 3-manifold topology. In: SCoG '11: Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry. 27th Annual Symposium on Computational Geometry (SoCG 2011), Paris, France, (145-152). 13-15 June 2011. doi:10.1145/1998196.1998219

  • Burton, Benjamin A. (2011). Detecting genus in vertex links for the fast enumeration of 3-manifold triangulations. In: ISSAC 2011: Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation. 36th International Symposium on Symbolic and Algebraic Computation [ISSAC], San Jose, CA, United States, (59-66). 8-11 June 2011. doi:10.1145/1993886.1993901

  • Burton, Benjamin A. (2011). The Pachner graph and the simplification of 3-sphere triangulations. In: SoCG '11 Proceedings of the 27th annual ACM Symposium on Computational Geometry. 27th ACM Symposium on Computational Geometry [SoCG], Paris, France, (153-162). 13-15 June 2011. doi:10.1145/1998196.1998220

  • Burton, Benjamin A. (2010). The complexity of the normal surface solution space. In: Proceedings of the 2010 Annual Symposium on Computational Geometry. 26th ACM Symposium on Computational Geometry [SCG], Snowbird, Utah, U.S.A., (201-209). 13-16 June 2010. doi:10.1145/1810959.1810995

  • Burton, Benjamin A. (2008). Informatics Olympiads: Challenges in programming and algorithm design. In: Gillian Dobbie and Bernard Mans, CRPIT - Computer Science 2008. Thirty-First Australasian Computer Science Conference (ACSC 2008), Wollongong, NSW, Australia, (9-13). 22-25 Jan 2008.

  • Sundaram, Shrikant, Bertok, Peter and Burton, Benjamin (2005). Secure group communication with distributed generation of private keys for ad-hoc networks. In: R. Sasaki, S. Qing, E. Okamoto and H. Yoshiura, Security and Privacy in the Age of Ubiquitous Computing: International Federation for Information Processing. IFIP TC11 20th IFIP International Information Security Conference, Chiba, Japan, (477-492). 3 May- 1 Jun 2005. doi:10.1007/0-387-25660-1_31

Grants (Administered at UQ)

PhD and MPhil Supervision

Current Supervision

  • Doctor Philosophy — Principal Advisor

    Other advisors:

  • Doctor Philosophy — Associate Advisor

    Other advisors:

Completed Supervision