8 problems

Subcube extremality conjecture. For all $\beta\ge\frac12$ and all $k\ge 1$,

Let $(X,\|\cdot\|_X)$ be a $K$-convex Banach space. For $n\in\mathbb{N}$, let $\operatorname{Deg}_{\le d}$ denote the space of functions $f:\{-1,1\}^n\to X$ whose Hamming cube Four…

Hamming-cube decay conjecture. For every fixed $c>2$, the quantity

All-codimension stability conjecture. The statement in Theorem $$ holds for all $k\in\mathbb P$, even with $n^\beta$ replaced by $2^n/\partial(|A|)$.

Maximal hybrid isoperimetric conjecture. If $|A|=a$, then

Fixed-error hybrid isoperimetric conjecture. There is a fixed constant $K$ such that, whenever $\mu(A)=1/2$,

Engbers–Galvin conjecture. For each fixed $q$,

Kahn's five-value range conjecture.