6 problems

Mubayi–Liu conjecture. Every number in $[0,4/9)$ is a jump, while every number in $[4/9,1)$ is a non-jump.

Polynomial-or-exponential growth conjecture. For any fixed $s,t,k$, the function $r_k(s,t;n)$ grows either polynomially or exponentially in $n$.

Iterated-tripartite characterization. The Ramsey number $r(F,n)$ is polynomial in $n$ if and only if $F$ is iterated tripartite.

Let $H$ be a $3$-uniform hypergraph, let $K_n^3$ be the complete $3$-uniform hypergraph on $n$ vertices, and let $r(H,K_n^3)$ be the corresponding Ramsey number. Call $H$ iterated…

Let $g_3(s)$ denote the maximum number of edges in an $s$-vertex iterated blowup of a $3$-uniform edge, and let $r_3(s,e;t)$ be the corresponding hypergraph Ramsey number. Conjectu…

Lagrangian-density conjecture. The Lagrangian density of $K_4^3\cup e$ is attained by $S_2(n)$ as $n\to\infty$. The conjecture is proposed as an approach to the unresolved Turán-de…