Henry Segerman

Department of Mathematics and Statistics

University of Melbourne

VIC 3010, Australia

Office: 165

Phone: +61 3 8344 9710

Email: segerman (at) unimelb (dot) edu (dot) au

Curriculum Vitae

Research Statement

Teaching Statement

Publication List

### 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.*3D printing for mathematical visualisation*, 7 pages, 9 figures,*Math. Intell.***34**(2012), no. 4, pages 56-62. The final publication is available at www.springerlink.com, at this page.*Sculptures in S*, with Saul Schleimer, 8 pages, 9 figures,^{3}*Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture*, pages 103-110.*Recent 3D printed sculptures*, 10 pages, 11 figures,*Hyperseeing*2011 Fall/Winter, 5 pages, 7 figures.*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.*Autologlyphs*, with P.-O. Dehaye,*Math. Intell.***26**(2004), no. 2, pages 37-39, and cover art.*100 prisoners and a lightbulb*, with P.-O. Dehaye and D. Ford,*Math. Intell.***25**(2003), no. 4, pages. 53-61.

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".

I designed the cover art and all illustrations for the book Blast into Math! by my friend Julie Rowlett, published January 2013.

### Talks

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 S
^{3}, 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).

### Press

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.

6 December 2011: I was interviewed by BBC Radio 5 about mathematical art and 3D printing. Here is the blogpost for the podcast. Here is the direct link to the mp3.

February 2008: I was interviewed on She Blinded Me With Science!, a show on the student radio station KVRX, talking about topology and juggling. You can listen to the interview here.

### Links

My Hilbert curve 3d print is available at vismath.eu, a German mathematics website and shop (English language version).

Go here for my personal website. Particularly math(s) related things: 3D printed sculpture, Autologlyphs, Escher's Printgallery at Stanford, Book Covers and Posters, T-shirt designs.

For keeping track of your and your friends' (lack of) mathematical progress: Ways to Go Wrong Tally Sheet.

My old University of Texas math website is here. My old Stanford math website is here.

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