Dr. Jonathan Spreer

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Dr. Jonathan Spreer

University of Queensland
School of Mathematics and Physics
Computational Geometry and Topology
Priestley #67, Cooper Rd
4072 St Lucia, QLD


+61-(0)7 / 3365 3116






since 2014Postdoctoral Research Fellow funded by the Australia-India Strategic Research Fund (AISRF).
Grant AISRF06660, at the School of Mathematics and Physics, University of Queensland.
2012 - 2013Postdoctoral Research Fellow at the School of Mathematics and Physics, University of Queensland.

2011Doctorate in natural sciences (Dr. rer. nat.) at the University of Stuttgart.
Dissertation: Blowups, slicings and permutation groups in combinatorial topologybib | http ] (Doctoral advisor: Prof. W. Kühnel).
2008Diploma in mathematics and computer science at the University of Stuttgart.
Diploma thesis at the Institute of Geometry and Topology, University of Stuttgart:
On the Topology of combinatorial 4-manifolds, in particular the K3-Surfacebib ] (Supervisor: Prof. W. Kühnel).
2007Maîtrise (french one year postgraduate diploma) in mathematics at the Université Pierre et Marie Curie in Paris.

Research areas

Computational geometry and topology
Parameterised complexity theory
3-manifold topology
Mathematical software

Current research projects

2015 - 2017 Benjamin A. Burton, Jonathan Spreer, Tractable topological computing: Escaping the hardness trap, Australian Research Council (ARC) Discovery Project 2015, DP150104108.

Computational topology is a young and energetic field that uses computers to solve complex geometric problems driven by pure mathematics, and with diverse applications in biology, signal processing and data mining. A major barrier is that many of these problems are thought to be fundamentally and intractably hard. This project will defy such barriers for typical real-world inputs by fusing geometric techniques with technologies from the field of parameterised complexity, creating powerful, practical solutions for these problems. It will shed much-needed light on the vast and puzzling gap between theory and practice, and give researchers fast new software tools for large-scale experimentation and cutting-edge computer proofs.
2014 - 2016 Benjamin A. Burton, Basudeb Datta, Jonathan Spreer, Nitin Singh, Building triangulations for fast topological computing, DIICCSRTE, Australia-India Strategic Research Fund (AISRF), Round 7, AISRF06660.

Computational topology is a young and fast-growing area of ICT, with roots in geometry and applications in biology, physics, computer vision and cosmology, in which real computations are often prohibitively expensive. We will overcome this by building "tight triangulations", highly efficient forms of input with which we can solve substantial problems cheaply using new and innovative heuristics. Outcomes will include practical software, with significant benefits spanning both ICT and mathematics.


simpcomp - A GAP toolbox for simplicial complexes -- simpcomp homepage.
Joint project with Felix Effenberger.
"Best Software Presentation Award" by the Fachgruppe Computeralgebra at the ISSAC 2010 in Munich.

Scientific work

[16] (with Bhaskar Bagchi, Benjamin A. Burton, Basudeb Datta and Nitin Singh) Efficient algorithms to decide tightness, 2014. 18 pages, 3 figures, arXiv:1412.1547 [math.GT]. [ bib | arXiv ]
[15] (with Bhaskar Bagchi and Basudeb Datta) Tight triangulations of closed 3-manifolds, 2014. 19 pages, 1 figure, arXiv:1412.0412 [math.GT]. [ bib | arXiv ]
[14] (with João Paixão) Random collapsibility and 3-sphere recognition, 2015. 18 pages, 6 figures, arXiv:1509.07607 [math.GT]. [ bib | arXiv ]
In press
[13] (with William Jaco, Jesse Johnson and Stephan Tillmann) Bounds for the genus of a normal surface, 2015. 39 pages, 25 figures. To appear in Geometry and Topology. [ bib | arXiv ]
[12] (with Benjamin A. Burton) Combinatorial Seifert fibred spaces with transitive cyclic automorphism group, 2015. 26 pages, 10 figures. To appear in Israel Journal of Mathematics. [ bib | arXiv ]
[6b] (with Benjamin A. Burton, Thomas Lewiner and João Paixão) Parameterized complexity of discrete Morse theory, 2015. 28 pages, 8 figures. To appear in ACM Transaction on Mathematical Software (TOMS). [ bib | arXiv ]
[11] (with Biplab Basak) Simple crystallizations of 4-manifolds, 2014. 22 pages, 7 figures. To appear in Advances in Geometry. [ bib | arXiv ]
[10] Necessary conditions for the tightness of odd-dimensional combinatorial manifolds. European J. Combin., 51:475-491, 2016. [ bib | arXiv | doi ]
[9] (with Benjamin A. Burton, Basudeb Datta and Nitin Singh) Separation index of graphs and stacked 2-spheres. J. Combin. Theory (A), 136:184-197, 2015. [ bib | arXiv | doi ]
[8] (with Benjamin A. Burton and Clément Maria) Algorithms and complexity for Turaev-Viro invariants. Automata, Languages, and Programming: 42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6-10, 2015, Proceedings, Part 1, pg. 281-293. [ bib | arXiv | doi ]
[7] Combinatorial 3-manifolds with transitive cyclic automorphism group. Discrete and Computational Geometry, 51(2):394-426, 2014. [ bib | arXiv | doi ]
[6a] (with Benjamin A. Burton, Thomas Lewiner and João Paixão) Parameterized complexity of discrete Morse theory. Proceedings of the Twenty-Ninth Annual Symposium on Computational Geometry (SoCG), pg. 127-136, 2013. [ bib | arXiv | doi ]
[5] (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. 78-87, 2013. [ bib | arXiv | doi ]
[4] (with Benjamin A. Burton) The complexity of detecting taut angle structures on triangulations. Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pg. 168-183, 2013. [ bib | arXiv | doi ]
[3] Partitioning the triangles of the cross polytope into surfaces. Beitr. Algebra Geom. / Contributions to Algebra and Geometry, 53(2):473-486, 2012. [ bib | http | arXiv | doi ]
[2] Normal surfaces as combinatorial slicings. Discrete Math., 311(14):1295-1309, 2011. [ bib | arXiv | doi ]
[1] (with Wolfgang Kühnel) Combinatorial properties of the K3 surface: Simplicial blowups and slicings. Exp. Math., 20(2):201-216, 2011. [ bib | http | arXiv | doi ]
Informal review only
[h] Random Collapsibility and 3-sphere recognition. To appear in Oberwolfach reports, 2015, 3 page extended abstract. [ bib ]
[g] (with Benjamin A. Burton) Computationally proving triangulated 4-manifolds to be diffeomorphic. 29th ACM Symposium on Computational Geometry, Young Researchers Forum, Collections of abstracts, 2013, pages 15-16. [ bib | arXiv ]
[f] (with Felix Effenberger) Simplicial blowups and discrete normal surfaces in the GAP package simpcomp. ACM Communications in Computer Algebra, 45(3):173 - 176, 2011. [ bib | arXiv | doi ]
[e] (with Felix Effenberger) simpcomp - a GAP toolbox for simplicial complexes. ACM Communications in Computer Algebra, 44(4):186 - 189, 2010. [ bib | doi ]
Mathematical software
[d] (with Felix Effenberger) simpcomp - A GAP package, Version 2.1.1, 2009-2015. [ bib | http ]
[c] 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 CG-Week 2014 at Kyoto University. June 10th, 2014 [ bib | arXiv | http ]
[b] Blowups, slicings and permutation groups in combinatorial topology. Logos Verlag Berlin, 2011. Dissertation. [ bib | http ]
[a] Über die Topologie von kombinatorischen 4-Mannigfaltigkeiten, insbesondere der K3-Fläche, 2008. Diplomarbeit. [ bib ]


Semester 1, 2015:MATH2301: Linear and Abstract Algebra and Number Theory
Semester 2, 2014:Reading course in Complexity Theory
Semester 1, 2014:MATH3302: Coding and Cryptography
Semester 1, 2013:MATH3302: Coding and Cryptography
Winter 2009/2010:Mathematics for Computer Scientists and Software Engineers I (Prof. Dr. Wolfgang Rump)
Summer 2009:Mathematics for Computer Scientists and Software Engineers II (Prof. Dr. Eberhard Teufel)
Winter 2008/2009:Mathematics for Computer Scientists and Software Engineers I (Prof. Dr. Eberhard Teufel)

Office hours

Thursday, 11.00 am - 12.00 pm