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My research interests are motivated by the study of manifolds (i.e., surfaces and their higherdimensional analogues). For this, I use a blend of techniques from mathematical fields such as lowdimensional topology and combinatorics, tools from computer science, such as parameterised complexity theory, as well as practical skills from algorithm design and the development of mathematical software. 

Current research projects  
2019  2021 
Hyam Rubinstein, Jonathan Spreer, Stephan Tillmann, Trisections, triangulations and the complexity of manifolds, Australian Research Council (ARC) Discovery Project 2019, DP190102259. 

Abstract:


Past research projects  
2015  2018 
Benjamin A. Burton, Jonathan Spreer, Tractable topological computing: Escaping the hardness trap, Australian Research Council (ARC) Discovery Project 2015, DP150104108. 

Abstract:


2014  2016 
Benjamin A. Burton, Basudeb Datta, Jonathan Spreer, Nitin Singh, Building triangulations for fast topological computing, DIICCSRTE, AustraliaIndia Strategic Research Fund (AISRF), Round 7, AISRF06660. 

Abstract: 

Publications  
My articles on arXiv.org 

Preprints  
(with Giulia Codenotti and Francisco Santos) Separationtype combinatorial invariants for triangulations of manifolds, 2018. 33 pages, 5 figures arXiv:1808.04220 [math.CO]. [ bib  arXiv ]  
(with William Jaco, Hyam Rubinstein and Stephan Tillmann) On minimal ideal triangulations of cusped hyperbolic 3manifolds, 2018. 30 pages, 16 figures, arXiv:1808.02836 [math.GT]. [ bib  arXiv ]  
(with Jorge Olarte and Francisco Santos) Short proof of two cases of Chvátal's conjecture, 2018. 3 pages, arXiv:1804.03646 [math.CO]. [ bib  arXiv ]  
(with William Jaco, Hyam Rubinstein and Stephan Tillmann) Z2Thurston Norm and Complexity of 3Manifolds, II., 2017. 21 pages, 10 figures, arXiv:1711.10737 [math.GT]. [ bib  arXiv ]  
(with Jorge Olarte, Francisco Santos and Christian Stump) Pure flag simplicial complexes and the ErdősKoRadoproperty, 2017. 23 pages, 2 figures, arXiv:1710.02518 [math.CO]. [ bib  arXiv ]  
(with Benjamin A. Burton and Basudeb Datta) The Pachner graph of 2spheres, 2017. 23 pages, 20 figures, 1 table, arXiv:1701.05144 [math.CO]. [ bib  arXiv ]  
(with João Paixão) Random collapsibility and 3sphere recognition, 2015. 18 pages, 6 figures, arXiv:1509.07607 [math.GT]. [ bib  arXiv ]  
Published  
(with Benjamin A. Burton and Clément Maria) Algorithms and complexity for TuraevViro invariants. Journal of Applied and Computational Topology, DOI 10.1007/s4146801800162, 121, 2018. [ bib  arXiv  doi ]  
(with Stephan Tillmann) Unravelling the Dodecahedral Spaces. 2016 MATRIX Annals In MATRIX Book Ser. (Springer, Cham), vol. 1, pg. 323347, 2018. [ bib  arXiv  doi ]  
(with Kristóf Huszár and Uli Wagner) On the treewidth of triangulated 3manifolds. 34nd International Symposium on Computational Geometry (SoCG 2018). In Leibniz International Proceedings in Informatics (LIPICS), vol. 99, pg. 46:146:15, 2018. [ bib  arXiv  doi ]  
(with Stephan Tillmann) Determining the trisection genus of orientable and nonorientable PL 4manifolds through triangulations. 34nd International Symposium on Computational Geometry (SoCG 2018). In Leibniz International Proceedings in Informatics (LIPICS), vol. 99, pg. 71:171:13, 2018. [ bib  arXiv  doi ]  
(with Clément Maria) A polynomial time algorithm to compute quantum invariants of 3manifolds with bounded first Betti number. Proceedings of the ACMSIAM Symposium on Discrete Algorithms (SODA 2017), pages 27212732, 2017. [ bib  arXiv ]  
(with Bhaskar Bagchi and Basudeb Datta) A characterization of tightly triangulated 3manifolds. European J. Combin., 61:133137, 2017. [ bib  arXiv  doi ]  
(with Benjamin A. Burton) Combinatorial Seifert fibred spaces with transitive cyclic automorphism group. Israel Journal of Mathematics, 214(2):741784, 2016. [ bib  arXiv  doi ]  
(with Benjamin A. Burton, Basudeb Datta and Nitin Singh) A construction principle for tight and minimal triangulations of manifolds. Experimental Mathematics, 27:2236, 2018. [ bib  arXiv  doi ]  
(with Clément Maria) Admissible colourings of 3manifold triangulations for TuraevViro type invariants. 24th Annual European Symposium on Algorithms (ESA 2016). In Leibniz International Proceedings in Informatics (LIPIcs), vol. 57, pg. 64:164:16, 2016. [ bib  arXiv  doi ]  
(with William Jaco, Jesse Johnson and Stephan Tillmann) Bounds for the genus of a normal surface. Geometry and Topology, 20(3):16251671, 2016. [ bib  arXiv  doi ]  
(with Bhaskar Bagchi, Benjamin A. Burton, Basudeb Datta and Nitin Singh) Efficient algorithms to decide tightness. 32nd International Symposium on Computational Geometry (SoCG 2016). In Leibniz International Proceedings in Informatics (LIPICS), vol. 51, pg. 12:112:15, 2016. [ bib  arXiv  doi ]  
(with Bhaskar Bagchi and Basudeb Datta) Tight triangulations of closed 3manifolds. European J. Combin., 54:103120, 2016. [ bib  arXiv  doi ]  
(with Biplab Basak) Simple crystallizations of 4manifolds. Advances in Geometry, 16(1):111130, 2016. [ bib  arXiv  doi ]  
(with Benjamin A. Burton, Thomas Lewiner and João Paixão) Parameterized complexity of discrete Morse theory. ACM Trans. Math. Softw., 42(1):24 pages, 2016. [ bib  arXiv  doi ]  
Necessary conditions for the tightness of odddimensional combinatorial manifolds. European J. Combin., 51:475491, 2016. [ bib  arXiv  doi ]  
(with Benjamin A. Burton, Basudeb Datta and Nitin Singh) Separation index of graphs and stacked 2spheres. J. Combin. Theory (A), 136:184197, 2015. [ bib  arXiv  doi ]  
(with Benjamin A. Burton and Clément Maria) Algorithms and complexity for TuraevViro invariants. Automata, Languages, and Programming: 42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 610, 2015, Proceedings, Part 1, pg. 281293. [ bib  arXiv  doi ]  
Combinatorial 3manifolds with transitive cyclic automorphism group. Discrete and Computational Geometry, 51(2):394426, 2014. [ bib  arXiv  doi ]  
(with Benjamin A. Burton, Thomas Lewiner and João Paixão) Parameterized complexity of discrete Morse theory. Proceedings of the TwentyNinth Annual Symposium on Computational Geometry (SoCG), pg. 127136, 2013. [ bib  arXiv  doi ]  
(with Benjamin A. Burton and João Paixão) Computational topology and normal surfaces: Theoretical and experimental complexity bounds. Proceedings of the Meeting on Algorithm Engineering and Experiments, pg. 7887, 2013. [ bib  arXiv  doi ]  
(with Benjamin A. Burton) The complexity of detecting taut angle structures on triangulations. Proceedings of the TwentyFourth Annual ACMSIAM Symposium on Discrete Algorithms, pg. 168183, 2013. [ bib  arXiv  doi ]  
Partitioning the triangles of the cross polytope into surfaces. Beitr. Algebra Geom. / Contributions to Algebra and Geometry, 53(2):473486, 2012. [ bib  http  arXiv  doi ]  
Normal surfaces as combinatorial slicings. Discrete Math., 311(14):12951309, 2011. [ bib  arXiv  doi ]  
(with Wolfgang Kühnel) Combinatorial properties of the K3 surface: Simplicial blowups and slicings. Exp. Math., 20(2):201216, 2011. [ bib  http  arXiv  doi ]  
Informal review only  
(with Clément Maria) Classification of Normal Curves on a Tetrahedron. 32nd Symposium on Computational Geometry, Young Researchers Forum, Collections of abstracts, 2016. [ bib  arXiv ]  
Random Collapsibility and 3sphere recognition. Computational Geometric and Algebraic Topology. In Oberwolfach reports, vol. 12(4), 26622665, 2015. [ bib  doi ]  
(with Benjamin A. Burton) Computationally proving triangulated 4manifolds to be diffeomorphic. 29th ACM Symposium on Computational Geometry, Young Researchers Forum, Collections of abstracts, 2013, pages 1516. [ bib  arXiv ]  
(with Felix Effenberger) Simplicial blowups and discrete normal surfaces in the GAP package simpcomp. ACM Communications in Computer Algebra, 45(3):173176, 2011. [ bib  arXiv  doi ]  
(with Felix Effenberger) simpcomp  a GAP toolbox for simplicial complexes. ACM Communications in Computer Algebra, 44(4):186189, 2010. [ bib  doi ]  
Mathematical software  
(with Felix Effenberger) simpcomp  A GAP package, Version 2.1.5, 20092016. [ bib  http ]  
Editorship  
Jonathan Spreer, Uli Wagner (Organisers), Benjamin A. Burton, Satoshi Murai, Eric Sedgwick, Henry Segerman. Collection of abstracts of the Workshop on Triangulations in Geometry and Topology at CG Week 2014 in Kyoto. 4 x 6 page extended abstracts. The workshop was held as part of CGWeek 2014 at Kyoto University. June 10th, 2014 [ bib  arXiv  http ]  
Theses  
Blowups, slicings and permutation groups in combinatorial topology. Logos Verlag Berlin, 2011. Dissertation. [ bib  http ]  
Über die Topologie von kombinatorischen 4Mannigfaltigkeiten, insbesondere der K3Fläche, 2008. Diplomarbeit. [ bib ]  
Selected talks  
Dec 2015 
Talk at the 39th Australasian Conference on Combinatorial Mathematics
and Combinatorial Computing, Brisbane, Australia. Title: Separation index of graphs and stacked 2sphere [ slides ] 

Oct 2015 
Talks at Institute for Science and Technology, Klosterneuburg, Austria;
Technische Universität Berlin, Germany;
Indian Institute of Science, Bangalore, India; and
Indian Statistical Institute, Calcutta, India. Title: Algorithms and complexity for TuraevViro invariants [ slides ] 

Oct 2015 
Presentation at Mathematical Research
Institute Oberwolfach, see extended abstract above. Title: Random collapsibility and 3sphere recognition [ slides (from the 2015 AustMS meeting in Adelaide) ] 

Jun 2015 
Talk at Freie Universität Berlin, Germany. Title: Parameterised complexity theory for topological problems [ slides (from the 2013 AustMS meeting in Sydney) ] 

Feb 2015 
Talk at University of Ulm, Germany. Title: Geometrie und Topologie im Computeralgebrasystem GAP [ slides ] 

May 2014 
Talk at the National Institute of Informatics Shonan Meeting on Knot theory, Algorithms, complexity and computation, Tokyo, Japan. Title: Tightness for triangulations [ slides (from the 2014 AustMS meeting in Melbourne) ] 

Apr 2014 
Talk at the Computational and Algorithmic Topology workshop (CATS), Sydney, Australia. Title: Bounds for the genus of a normal surface [ slides ] 

Dr Jonathan Spreer  The University of Sydney  School of Mathematics and Statistics  Email: jonathan.spreer@sydney.edu.au 