4 problems

Exact spectral threshold conjecture. If

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

Let $X_1,\dots,X_r$ be sets of size $n$, and let $\iota(t,n;r)$ be the maximum size of a $t$-intersecting family $\mathcal{F}\subseteq X_1\times\dots\times X_r$, where two sequence…

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…