8 problems

Let $G$ be a compact group equipped with its Haar probability measure, and let a Kedlaya set be a set of the form … where $G$ acts on a set $X$, $B\subseteq X$, and $x\in X$. A mea…

Stability conjecture. For each $\delta>0$, there exists $\varepsilon>0$ such that, whenever $S\subset\mathcal{F}$ is product-free and

Extremal 3-product-free set conjecture. One of the following holds: either the letters of $\mathcal{A}$ can be labelled by $\mathbb{Z}/3\mathbb{Z}$ so that $S$ is contained in the…

Leader–Letzter–Narayanan–Walters conjecture. If $S\subset\mathcal{F}$ is product-free and $d^{\ast}(S)=1/2$, then

Upper Banach density conjecture. No product-free subset $S\subset\mathbf{F}_{\mathscr{A}}$ has upper Banach density exceeding

Uniqueness conjecture. If $S\subset\mathcal{F}_{\mathscr{A}}$ is product-free and

Classification conjecture. The group $G$ is filled if and only if $G$ is either an elementary abelian $2$-group or one of

Let $G$ be a finite group, let $\mathbb{F}$ be a field, and let $X_1,\dots,X_k$ be subspaces of the group algebra $\mathbb{F}[G]$ satisfying … Define $M_k(G)$ to be the minimum, ov…