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various notes

• The first two installations of a series of notes on the density increment method from fall 2024: [A5.1] Meshulam's theorem, [A5.2] Roth's theorem. I think the heuristic discussion in these notes are one of the best available. Unfortunately I did not continue this series of notes.
• [A4] Slides from a private presentation in summer 2025 on amenability with a view towards pointwise ergodic theorems, including a proof of equivalent characterizations of amenability (following Kerr and Li) and a counterexample of Emerson.
• A self-contained exposition of the main result in Ben Green’s paper Arithmetic Progressions in Sumsets (GAFA 2002). Written as the final project of the course Topics in Additive Combinatorics in Spring 2024. [A3] pdf. Includes proofs of Bernstein, Khintchine, Rudin inequalities and Chang’s lemma also. Comments: The definition of dissociativity here can be weakened to "every element of G has at most one representation as the sum of elements of A" without changing any of the proofs.
• A summary of Ben Green’s notes on quadratic Fourier analysis, written for the summer school on analysis of multiple ergodic averages at Kopp in summer 2023. Joint with Nihan Tanısalı. Many details omitted due to space constraints. [A2.1] summary, [A2.2] slides. Comments: The summary contains a 1-page synopsis of the U³ inverse theorem, with some elaboration in the slides.
• A self-contained exposition of a proof of Roth’s theorem. I wrote this as the “final report” of my independent study under Asgar Jamneshan in spring 2023. [A1] pdf. There are very few known typos, but often the correction is obvious so I didn’t bother to fix them. Comments: There is not much to learn here unless you are looking for a "speedrun" towards Roth.