3 problems

Inverse conjecture for the directional uniformity norms. If $f\colon G\to\mathbb{D}$ satisfies $\|f\|_{\mathsf{U}(H_1,\dots,H_r)}\geq c$, then there exist functions…

Uniformity conjecture. Then, for every $s\geq 1$, there exists $c_s>0$ such that

Infinite-set extension conjecture. The same conclusion holds when $Z$ is infinite.