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This is a long overdue page providing a kind of index to various unpublished or unpublishable notes that I have written. You may also wish to look at my papers and preprints, which include several survey articles, or my Cambridge Part III courses.

In April 2002 I gave 3 lectures on the Structure Theory of Set Addition in Edinburgh. I lectured on this topic again in MIT in 2005, an undertaking which led to some supplementary notes on Progressions and Convex Geometry. Armed with both of these sets of notes, the reader should have a fairly complete grasp of Chang's bounds for Freiman's theorem. At some point in the near future the notes will be coalesced into the Edinburgh-MIT notes on Freiman's theorem.

Here are some notes on the Bourgain-Katz-Tao sum-product theorem, which I also lectured on at MIT.

At the start of my PhD in 1999 I wrote some notes on Bourgain's bound for 3-term progressions, his work on arithmetic progressions in sumsets and the Heath-Brown-Szemeredi bound for 3-term progressions. Since I wrote these notes I have learnt quite a lot, and furthermore all of these results have now been improved. However people occasionally ask me for these notes, which is why I have made them available here. I have not updated them to take account of recent developments.

A long time ago, in 1998, I entertained notions of becoming a proper number theorist. Around that time I wrote an essay on why is exceptionally close to an integer. I have been asked for a copy of this (well, OK, only once) so I've put it up here for amusement.

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