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After 8 years as a mathematician, I am currently doing post-doctoral research as a theoretical neuroscientist at ENS in Paris.

I am currently working on a paper, based on chapter 5 of my thesis, which I intend to submit to the journal Experimental Mathematics. This paper will present the numerical evidence I gathered during my PhD for the conjectures that the boundary of the Maskit slice is twisting (spiralling infinitely) almost everywhere, and has Hausdorff dimension less than 1.25.

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.

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.

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).

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.