3 problems

Exact spectral threshold conjecture. If

For integers $r\ge 3$ and $n_1\ge\dots\ge n_r\ge 2$, let $X_1,\dots,X_r$ be disjoint sets with $|X_i|=n_i$. Define $m_0(s,n_1,\dots,n_r)$ as the maximum size of a family…

Mycroft's constant-error conjecture. There exists a constant $C=C(F)$ such that the error terms in $$ can be replaced by $C$.