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.
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.
Tractable topological computing: Escaping the hardness trap
(2015–2023) ARC Discovery Projects
Building triangulations for fast topological computing
(2014–2017) Department of Innovation, Industry, Science and Research - Australia-India Strategic Research Fund
(2014–2017) ARC Discovery Projects
Computational complexity of topological problems
Doctor Philosophy
Practical computation of topological invariants
Master Philosophy
Computational 4-manifold topology
Doctor Philosophy
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.
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
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
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, 1-19. doi: 10.1080/10586458.2022.2161676
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
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
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
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
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
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
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
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
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
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
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.
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
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 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
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
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
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
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
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
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
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
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
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
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.
Get involved! The IOI workshop 2010, its goals and results
Pohl, Wolfgang, Burton, Benjamin A., Dagienė, Valentina, Fakcharoenphol, Jittat, Forišek, Michal, Hiron, Mathias, Opmanis, Mārtiņš, Skūpas, Bronius and van der Vegt, Willem (2010). Get involved! The IOI workshop 2010, its goals and results. Olympiads in Informatics, 4, 158-169.
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
Quadrilateral-octagon coordinates for almost normal surfaces
Burton, Benjamin A. (2010). Quadrilateral-octagon coordinates for almost normal surfaces. Experimental Mathematics, 19 (3), 285-315. doi: 10.1080/10586458.2010.10390625
Converting between quadrilateral and standard solution sets in normal surface theory
Burton, Benjamin A. (2009). Converting between quadrilateral and standard solution sets in normal surface theory. Algebraic and Geometric Topology, 9 (4), 2121-2174. doi: 10.2140/agt.2009.9.2121
Breaking the routine: Events to complement informatics olympiad training
Burton, Benjamin A. (2008). Breaking the routine: Events to complement informatics olympiad training. Olympiads in Informatics, 2, 5-15.
Creating informatics olympiad tasks: Exploring the black art
Burton, Benjamin A. and Hiron, Mathias (2008). Creating informatics olympiad tasks: Exploring the black art. Olympiads in Informatics, 2, 16-36.
Enumeration of non-orientable 3-manifolds using face-pairing graphs and union-find
Burton, Benjamin A. (2007). Enumeration of non-orientable 3-manifolds using face-pairing graphs and union-find. Discrete and Computational Geometry, 38 (3), 527-571. doi: 10.1007/s00454-007-1307-x
Informatics olympiads: Approaching mathematics through code
Burton, Benjamin A. (2007). Informatics olympiads: Approaching mathematics through code. Mathematics Competitions, 20 (2), 29-51.
Observations from the 8-tetrahedron nonorientable census
Burton, Benjamin A. (2007). Observations from the 8-tetrahedron nonorientable census. Experimental Mathematics, 16 (2), 129-144. doi: 10.1080/10586458.2007.10128994
Structures of small closed non-orientable 3-manifold triangulations
Burton, Benjamin A. (2007). Structures of small closed non-orientable 3-manifold triangulations. Journal of Knot Theory and Its Ramifications, 16 (5), 545-574. doi: 10.1142/S0218216507005439
Efficient enumeration of 3-manifold triangulations
Burton, Benjamin A. (2004). Efficient enumeration of 3-manifold triangulations. The Australian Mathematical Society Gazette, 31 (2), 111-117.
Face pairing graphs and 3-manifold enumeration
Burton, Benjamin A. (2004). Face pairing graphs and 3-manifold enumeration. Journal of Knot Theory and Its Ramifications (JKTR), 13 (8), 1057-1101. doi: 10.1142/S0218216504003627
Introducing Regina, the 3-manifold topology software
Burton, Benjamin A. (2004). Introducing Regina, the 3-manifold topology software. Experimental Mathematics, 13 (3), 267-272.
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
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
Tabulation of knots and 3-manifolds
Burton, Benjamin (2019). Tabulation of knots and 3-manifolds. The University of Queensland. (Dataset) doi: 10.48610/3bb4c69
Tractable topological computing: Escaping the hardness trap
(2015–2023) ARC Discovery Projects
Building triangulations for fast topological computing
(2014–2017) Department of Innovation, Industry, Science and Research - Australia-India Strategic Research Fund
(2014–2017) ARC Discovery Projects
Australia Japan Emerging Research Leaders Exchange Program (ERLEP) 2012
(2013) Department of Innovation, Industry, Science and Research
Algorithmic methods in combinatorial topology
(2012–2013) Go8 Australia - Germany Joint Research Co-operation Scheme
Generic complexity in computational topology: Breaking through the bottlenecks
(2011–2013) ARC Discovery Projects
Complexity in topology: is unknot recognition as difficult as it seems?
(2011–2012) UQ Early Career Researcher
New-generation parallel-computing cluster for the mathematical and physical sciences
(2011) UQ Major Equipment and Infrastructure
ResTeach 2011 0.1 FTE School of mathematics and Physics
(2011) UQ ResTeach
UQ Travel Awards Category 1 - Mr Mathias Hiron
(2011) UQ Travel Grants Scheme
Algorithms and computation in four-dimensional topology
(2010–2015) ARC Discovery Projects
Fast algorithms for string processing in cryptography and bioinformatics
(2010–2011) UQ New Staff Research Start-Up Fund
Computational complexity of topological problems
Doctor Philosophy — Principal Advisor
Other advisors:
Practical computation of topological invariants
Master Philosophy — Principal Advisor
Computational 4-manifold topology
Doctor Philosophy — Principal Advisor
Other advisors:
Applying Operations Research techniques to Pure Mathematics problems
Doctor Philosophy — Associate Advisor
Other advisors:
Graph Algorithms and Network Motifs: Tools for Text Exploration
(2016) Doctor Philosophy — Principal Advisor
Other advisors:
Information processing in the developing zebrafish brain
(2020) Doctor Philosophy — Associate Advisor
Latin Squares and Related Structures
(2016) Doctor Philosophy — Associate Advisor
Other advisors:
(2014) Doctor Philosophy — Associate Advisor
Other advisors:
Orthogonal Arrays; Enumeration and Applications
(2013) Doctor Philosophy — Associate Advisor
Other advisors: