7 problems

Let $d\ge 2$ and let $\mathcal{H}$ be a $(d-1)$-partite $(d-1)$-uniform hypergraph. For $k\in\mathbb{N}$, let $\mathcal{H}(k)$ be the $d$-partite $d$-uniform hypergraph whose $d$th…

For an $r$-uniform linear cycle $C^r_{2\ell+1}$ of odd length $2\ell+1$, let $s(C^r_{2\ell+1})$ denote its Sidorenko gap. Odd linear-cycle Sidorenko-gap conjecture. For $r\geq 3$ a…

For an $r$-partite $r$-graph $F$, let $s(F)$ be its Sidorenko gap, defined by … Assume $r\geq 3$ and … for some $0<\alpha<r-1$. The hypergraph supersaturation conjecture. There exi…

Let $F$ be an $r$-uniform hypergraph and let $k$ be the uniformity of the clique $K_{k+1}^k$. Distinct edges of $F$ satisfy the $k$-linear condition when $|e\cap f|<k$ for every pa…

Let $F$ be a bipartite graph, and let $\mathrm{E}^r(F)$ denote its $r$-uniform expansion: each edge of $F$ is extended to an $r$-edge by adding new vertices. An $r$-graph is Sidore…

Directed Sidorenko conjecture. If $B$ is a bipartite oriented graph with a homomorphism $B\to\vec K_2$, then $B$ has the directed Sidorenko property. This is a directed analogue of…

Retract-smoothness conjecture. If $H$ is a Sidorenko graph and $T$ is a retract of $H$, then $T$ is smooth in $H$.