6 problems

Tomon’s conjecture. The inequality $\mu_p(\mathcal G)\leq p^t$ holds, with equality if and only if $\mathcal G\cong\mathcal F_0^t$.

Three-fold cross-intersection product-measure conjecture. If $\mathcal A_1,\mathcal A_2,\mathcal A_3$ are 3-cross intersecting, then

Conjecture on optimal stability constants. There exists a constant $C_p'$ such that the inequality in case (ii) of the theorem can be replaced by

Refinement of the biased $r$-wise intersection threshold conjecture. The condition

Biased extension conjecture. These biased results should extend to $1/2<p\leq 3/4$. This conjecture was disproved by Keller and Lifschitz, so the proposed extension is false.

Improved threshold conjecture. The condition in Theorem Main can be replaced by