2 problems

Georgakopoulos et al.'s minimum-codegree conjecture. Every $n$-vertex $k$-graph with minimum codegree at least $n/k$ contains a spanning $(k-1)$-sphere.

Georgakopoulos–Haslegrave–Montgomery–Narayanan's conjecture. If $\delta^{\ast}(H)\geqslant n/2$, then $H$ contains a spanning copy of $\mathbb{S}^{k-1}$.