Papers and preprints
Geometry and Topology
1-efficient triangulations and the index of a cusped hyperbolic 3-manifold, with Stavros Garoufalidis, Craig D. Hodgson and J. Hyam Rubinstein, 60 pages, 27 figures, arXiv:1303.5278 [math.GT] (2013).
Triangulations of hyperbolic 3-manifolds admitting strict angle structures, with Craig D. Hodgson and J. Hyam Rubinstein, 22 pages, 9 figures, Journal of Topology 5 (2012), no.5, pp. 887-908.
A generalisation of the deformation variety, 66 pages, 26 figures, Algebraic and Geometric Topology 12 (2012), no. 4, pp. 2179-2244.
Pseudo-developing maps for ideal triangulations I: Essential edges and generalised hyperbolic gluing equations, with Stephan Tillmann, 18 pages, 8 figures, Topology and Geometry in Dimension Three: Triangulations, Invariants, and Geometric Structures (Proceedings of the Jacofest conference), AMS Contemporary Mathematics 560 (2011), pp. 85-102.
Veering triangulations admit strict angle structures, with Craig D. Hodgson, J. Hyam Rubinstein and Stephan Tillmann, 15 pages, 9 figures, Geometry & Topology 15 (2011), pp. 2073-2089.
Incompressible surfaces in handlebodies and boundary compressible 3-manifolds, with J. Nogueira, 31 pages, 14 figures, Topology and its Applications 158 (2011), no. 4, pp. 551-571.
Detection of incompressible surfaces in hyperbolic punctured torus bundles, 52 pages, 25 figures, Geometriae Dedicata 150 (2011), no. 1, pp. 181-232.
On spun-normal and twisted squares surfaces, 15 pages, 13 figures, Proc. Amer. Math. Soc. 137 (2009), pp. 4259-4273.
Mathematical Art and Recreational Mathematics
Triple gear, with Saul Schleimer, 8 pages, 19 figures, to appear in Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture.
Developing fractal curves, with Geoffrey Irving, 21 pages, 22 figures.
How to print a hypercube, 5 pages, 9 figures, Math Horizons 20 (Feb 2013), issue 3, pages 5-9.
Sculptures in S3, with Saul Schleimer, 8 pages, 9 figures, Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture, pages 103-110.
Fractal graphs by iterated substitution, 24 pages, 20 figures, Journal of Mathematics and the Arts (© Taylor and Francis, available online at: http://www.tandfonline.com), 5 (2011), no. 2, pages 51-70.
The Sunflower Spiral and the Fibonacci metric, 4 pages, 4 figures, Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture, pages 483-486.
My Ph.D. thesis is available here (submitted May 2007). It bears a striking resemblance to the paper "Detection of incompressible surfaces in hyperbolic punctured torus bundles".
Slides and notes from some of my talks (see my CV for more):
- Puzzling the 120-cell, August 2013, Video.
- Triple gear, July 2013, Video.
- Fractal curves, 4-dimensional puzzles and unlikely gears, April 2013.
- Fractals and how to make a Sierpinski Tetrahedron, November 2012. The activity following this talk is to build a large Sierpinski tetrahedron from 256 small tetrahedra, which can be made from 128 copies of this page.
- Using Mathematica and Rhinoceros to produce 3D printed mathematical models - workshop notes, Mac/Windows, November 2012. Also available: workshop materials.
- Sculptures in S3, July 2012, Video.
- Some Mathematical Sculptures, January 2012.
- Triangulations of hyperbolic 3-manifolds admitting strict angle structures, January 2012.
- A generalisation of the deformation variety, Oct 2010.
- The Sunflower Spiral and the Fibonacci Metric, Jul 2010.
- When is a knot not a knot?, Jan 2010.
- The Mathfest 2009 Poster Image, Mathematical Art, Design and Education in Second Life, Aug 2009.
I also showed a video at the start of the talk and another at the end.
- Drawing knots using computers, Jul 2009.
- Extending the deformation variety, Nov 2008.
- Ideal triangulations and components of the Character variety, Nov 2007.
On 23rd February 2008 I gave a talk to the University of Texas Mathematics Department's Saturday Morning Math Group (for an audience of around 200 high school students from nearby schools in the area), you can see a video of it here (scroll down to my talk).
15 March 2013: Megan Gambino wrote a blog post for Smithsonian magazine on my 3D printed sculpture.
31 October 2012: Evelyn Lamb wrote a blog post for Scientific American on the "30-cell puzzle", a 3D printed puzzle by Saul Schleimer and me based on the 120-cell, one of the regular 4-dimensional polytopes.
23 August 2012: My sculpture "Dual Half 120- and 600-Cells" (joint work with Saul Schleimer) won the "Best Use of Mathematics" prize (one of four prizes awarded) at the Bridges conference 2012. It was featured in a slide show on the Scientific American website.
January 2012: I was interviewed for an article in the "Voice", a publication put out by the University of Melbourne, on "The language and art of maths". Here is the article. The online version of the article is missing the image (shown here) that went with the article. Alternatively, here is a pdf of the whole publication, which includes the article (on page 4) together with the photograph.
For keeping track of your and your friends' (lack of) mathematical progress: Ways to Go Wrong Tally Sheet.
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