Here are some expository notes I have written, on various topics. They are mainly written for me, to help focus my thoughts when learning a new topic or trying to understand a proof. I've put them here since they may be helpful to others. They are all 'living documents', and will be expanded/edited without warning. If you have any comments or corrections, let me know by email.

Caution: while I have tried to be clear and complete, when writing these I had in mind an audience of "myself in six months time when I've forgotten all this again", so there is an idiosyncratic choice of what notation to define, what steps of a proof to explain in detail, etc.

• Polynomial Method reading rack (a collection of links and papers relating to the Croot-Lev-Pach polynomial method)
• Entropy
• Bounds on families with small VC-dimension
• Additive energy amplification (exposition of results of Katz-Koester and Schoen)
• Almost-periodicity
• Hovanskii's theorem
• Finite groups
• Cauchy-Schwarz complexity
• Irrationality of zeta constants
• Hypothesis K of Hardy and Littlewood