8 problems

Nearly linear extremal-function conjecture. The function $\mathrm{ex}_e(F,n)$ is nearly linear if and only if $F$ is an orderly bipartite forest with singletons that is not isomorp…

Let $u$ be a forbidden sequence and let $\operatorname{Sat}(n,u)$ denote the saturation function for sequences over an $n$-letter alphabet. A sequence is $u$-saturated if it is $r$…

Let $n$ be the number of polynomials, and let $k$ be their maximum degree. The complexity of the lower envelope is the maximum possible length of the sequence of polynomials appear…

Nonlinear containment conjecture. Every nonlinear sequence $\sigma$ contains $ababa$, $abcacbc$, or some sequence morally equivalent to $abcacbc$.

Doubling conjecture. In general, it is not true that

Let $t_1,t_2,\dots,t_s$ be integers and let $t=\max(t_1,t_2,\dots,t_s)$. For positive integers $r,k,n$, let $\operatorname{Ex}_r(12^{t_1}3^{t_2}\dots s^{t_{s-1}}(s+1)^{t_s}1,k,n)$…

Alon–Kaplan–Nivasch–Sharir–Smorodinsky conjecture. The upper bounds for odd orders are tight; equivalently,

Let $\Gamma_1$ be a collection of $n$ semi-infinite Jordan curves in the plane, where any two curves intersect at most $s$ times, for some fixed constant $s>0$. Let $A(\Gamma_1)$ b…