12 problems

Polynomial Gowers inverse conjecture. For every fixed $d$, the function $\Phi$ can be chosen to satisfy

Let $A$ be a set of $k\geq 4$ positive integers, and let $h$ be an integer with $3\leq h\leq k-1$. The restricted signed $h$-fold sumset is denoted by $h^{\wedge}_{\pm}A$. Bhanja–K…

Let $A\subset\mathbb{Z}$ be a finite set of size $N$, and let $K>0$. Write $1_A$ for its indicator and define … A finite arithmetic progression is a finite subset of $\mathbb{Z}$ w…

Let $I$ be the interval in the paper, let $I_\delta$ denote its interior subinterval at distance $\delta>0$ from the boundary, and let $I_\delta^0$ be the corresponding interior do…

Let $P_1,\dots,P_s\in\mathbb{Z}[x]$ be linearly independent polynomials that vanish at zero. Let $f_\omega:\mathbb{Z}/N\mathbb{Z}\to\mathbb{C}$ be one-bounded functions, and define…

Symmetrization conjecture. If

Griesmer's conjecture. Under these hypotheses, such compact subsets $A'$ and $B'$ exist. This conjecture proposes an inverse theorem for near equality in Kneser's inequality that e…

Let $A$ be a finite set of integers, and write $A-A=\{a-a':a,a'\in A\}$. Small-doubling structural conjecture. There exists a natural number $K$ such that, whenever $|A|\ge K$ and…

Let $d$ and $R$ be fixed, and set $s:=\lfloor R\rfloor+1$. For Bernoulli random variables, let $p(d,R,\operatorname{Ber},n)$ denote the maximal probability that the associated sum…

Károlyi's inverse Erdős–Heilbronn conjecture. The equality

Let $G$ be a nonabelian group, and let $A$ and $B$ be subsets whose restricted product set consists of products $ab$ with the factors subject to the distinctness restriction. Károl…

Let $p$ be a prime, let $k$ be a positive integer, and let $f:\mathbb{F}_p^n\rightarrow\mathbb{C}$ be a function bounded in magnitude by $1$. Suppose that $f$ has large $U^{k+1}$ n…