4 problems

For an integer $r\geq2$, let $\operatorname{ind}_r(k,\ell)$ denote the limiting maximum proportion of $k$-vertex subsets inducing exactly $\ell$ edges in an $r$-uniform hypergraph.…

Generic-value stability conjecture. There exists $\delta_r>0$ such that

Stability conjecture away from binomial values. Although the constant $1/e$ in the general bound is best possible, it should be improvable whenever

Kwan–Sudakov–Tran strengthened dense inducibility conjecture. There is a constant $C_r$, depending only on $r$, such that