A selection of notes I've written up; available here partially in case others find them useful, but mainly so that I can access them from any computer with internet access. If you have any comments, suggestions, or typos while reading them to report, please email me.
Talks
Polynomials rings in additive combinatorics -- given at the Paul Turán Memorial Conference in Mathematics, Budapest 26/08/11.
Notes
I wrote my fourth-year dissertation on the Green-Tao theorem on arithmetic progressions within the primes. There is no original mathematics in there, but it is the first place where the proof is given including the recent simplifications of Gowers, Green and Tao.
A brief summary of many of the most commonly used tricks and methods used in additive combinatorics -- these come under the heading of 'things which are obvious in hindsight but cause hours of confusion if I forget them' so I wrote them down to avoid this. Currently includes: dyadic pigeonholing, Plunnecke inequalities, Cauchy-Schwarz, large families principle, and spectrum estimates.
Various LaTeX tips and tricks.
Talks
Polynomials rings in additive combinatorics -- given at the Paul Turán Memorial Conference in Mathematics, Budapest 26/08/11.
Notes
I wrote my fourth-year dissertation on the Green-Tao theorem on arithmetic progressions within the primes. There is no original mathematics in there, but it is the first place where the proof is given including the recent simplifications of Gowers, Green and Tao.
A brief summary of many of the most commonly used tricks and methods used in additive combinatorics -- these come under the heading of 'things which are obvious in hindsight but cause hours of confusion if I forget them' so I wrote them down to avoid this. Currently includes: dyadic pigeonholing, Plunnecke inequalities, Cauchy-Schwarz, large families principle, and spectrum estimates.
Various LaTeX tips and tricks.