Hypergraphs with infinitely many extremal constructions by Jianfeng Hou, Heng Li, Xizhi Liu, Dhruv Mubayi, Yixiao Zhang

“…This is one of the most famous open problems in extremal combinatorics. It is conjectured that the extremal density is 5/9, but a sign that the conjecture is hard is that if the conjecture is true, the example just presented is not _the_ extremal example, but merely _an_ extremal example, as it is now known that there is an infinite family of 3-uniform hypergraphs with no cliques of size 4 and with asymptotic density 5/9. …”
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Gowers norms for automatic sequences by Jakub Byszewski, Jakub Konieczny, Clemens Müllner

“…There are several situations in additive and extremal combinatorics where it is useful to decompose an object $X$ into a "structured" part $S(X)$ and a "quasirandom" part $Q(X)$. …”
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