8 problems

Small-doubling abelianity conjecture. If

Three-set small-doubling conjecture. If $|S^2|\leq 3k-4$, then $\langle S\rangle$ is abelian.

Two-set small-doubling conjecture. If $|S^2|\leq 3k-3$, then $\langle S\rangle$ is abelian.

Let $n$ be a positive integer, let $\mathbb{Z}_n$ be the cyclic group of order $n$, and let $A\subseteq\mathbb{Z}_n$. For a subset $S\subseteq\mathbb{Z}_n$, write $2S=S+S$. Small-d…

Let $[n]=\{1,\ldots,n\}$, and let $s$ and $K$ be parameters. A set $J\subset[n]$ has doubling constant at most $K$ when $|J+J|\leq K|J|$. Alon–Balogh–Morris–Samotij conjecture. For…

Low-dimensional subset conjecture. There is a subset $X \subseteq A$ such that

Almost-homomorphism formulation of the Polynomial Freiman-Ruzsa conjecture. Is it true that $f=\widetilde f+g$, where $\widetilde f:\mathbb{F}_2^n\rightarrow\mathbb{F}_2^{n'}$ is l…

Let $F(K)$ and $G(K)$ be the functions introduced earlier in the paper for measuring the linear structure of finite binary sets with doubling parameter $K$. The piecewise-linearity…