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Research

Conference timer

I wrote a handy little HTML/Javascript page that can be used as a timer at conferences.

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Quasiregular dynamics

With Alastair Fletcher, I wrote some code for producing images of Mandelbrot and Julia sets for quasiregular mappings.

The twisting boundary of the Maskit slice

This is an unfinished paper, based on chapter 5 of my thesis.

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Maskit

I wrote some software to draw pictures of the Maskit slice, including pleating rays. It allows you to zoom in as far as numerical precision allows, and it has a nice graphical interface (illustrated below). If you're interested in how it works, take a look here. You can export the pictures as postscript files or into Mathematica. You can also export to binary or ASCII format, but I haven't provided any documentation on these. The software runs on Windows, and requires DirectX (which should be installed on almost all versions of Windows now). If you want to try to compile and run this on Linux, let me know. It is possible, but it takes a bit of work and since each version of Linux is different I can't provide a precompiled version. You can download the software here (360k) as a zipped folder.


Programs

As part of my thesis, I wrote some software to draw pictures of the Maskit slice. If you only want to produce pictures of the Maskit slice, you should use the graphical version of this software.


Spirals in the boundary of quasifuchsian space

My paper Spirals in the boundary of slices of quasifuchsian space was published by the Journal of Conformal Geometry and Dynamics. The abstract reads:
We prove that the Bers and Maskit slices of the quasifuchsian space of a once punctured torus have a dense, uncountable set of points in their boundaries about which the boundary spirals infinitely.

You can download my version (slightly different to the published version) in PDF format (340k).


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Thesis

My PhD thesis is entitled Boundaries of slices of quasifuchsian space. As well as the results from my paper it has some conjectural results about the boundary of the Maskit and Bers slices. On the basis of very strong numerical evidence, I conjecture that the boundary spirals infinitely almost everywhere and that the Hausdorff dimension of the Maskit slice is less than 1.25 (and more likely to be closer to 1.05). You can download it in PDF (1.8MB) format only. The computer programs that come with are available on this page. In order to save some trees, the version on this page is a single spaced version with small margins, unlike the printed version which is double spaced with large margins. In order to save space on my webpage, this version doesn't have the highest quality versions of some of the figures produced by David Wright. If you're interested, email me or him.


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