5 problems

Erdős–Hajnal–Rado conjecture. For the relevant uniformities $k$,

Let $r_4(5,n)$ be the smallest integer $N$ such that every $N$-vertex $4$-uniform hypergraph contains either a copy of $K_5^{(4)}$ or an independent set of size $n$. Mubayi–Suk con…

Let $k$ be a field of characteristic zero, let $V_d$ be a $k$-vector space of dimension $d$, and let $\Lambda^{S^r}_{V_d}$ be the graded quotient constructed from…

Let $k$ be a field of characteristic zero, let $V_d$ be a $k$-vector space of dimension $d$, and let $\Lambda^{S^3}_{V_d}$ be the graded vector space whose degree-$n$ component is…

Hypergraph independent-set extremal conjecture. If $\mathcal{G}$ is a $d$-regular $r$-graph on $n$ vertices, then