Expositions

Most of these arose from extended efforts to understand difficult papers in areas that interest me. My aim in each case was to take a paper, digest it, and then write it up in as coherent and comprehensible a manner as possible, giving full details of any background topics that I was unfamiliar with. No offence is intended to the authors of these papers; in fact, quite the contrary. Clicking on the name of an essay will produce an abstract.

Some of my files have been zipped up. For the reader who is not familiar with unzipping, I advise typing (in UNIX) "gzip -d file.dvi.gz".

Title Pages Download
Kakeya Problem and Number Theory 78 gzipped dvi
Bourgain on 3-term APs 34 pdf
Szemerédi on 3-term APs 7 pdf
Arithmetic Progressions in Sumsets 15 gzipped dvi
e^{\pi \sqrt{163}} 47 gzipped dvi

Notes on Sieve Theory

In (some of) my spare time I'm trying to understand what sieves are all about. These notes will be updated every now and then as I get my head around new topics, the eventual aim being to write notes that would serve for a decent length course on the subject.

Title Pages Download
Large Sieve for Absolute Beginners 6 dvi
The Brun Sieve 4 dvi
The Selberg Sieve 11 dvi
A Primer on Dirichlet Characters 7 dvi
Zero Density Estimates and the Bombieri-Vinogradov Theorem   To be written

Miscellaneous Other Notes

Some of these were written because I was being particularly unintelligent and needed to write myself a remedial guide to a particular topic. Others were written for my friends after I had spent a long time understanding some badly lectured topic. Still others were written because I felt like it.

Title Pages Download
Bernstein's Inequality and Hoeffding's Inequality 5 pdf
Group Cohomology 1 5 dvi
Group Cohomology 2 5 dvi
Universal Enveloping Algebras 5 dvi
Fourier Analysis and the Zeta Function 6 dvi
Stationary Phase and Van der Corput 8 dvi
Interpolation and Phragmen-Lindelof 3 dvi
An argument of Cameron and Erdos 2 pdf