4 problems

Sullivant's conjecture. For any finite abelian group $G$, $\phi(G)\leq |G|$.

Let $\mathcal{G}$ be a finite group acting on a finite set of states, and let $L$ be a labeling function that is symmetric and $\mathcal{G}$-compatible. A labeling is friendly when…

Finite-complexity conjecture. For any finite (not necessarily abelian) group $G$, $\phi(G)$ is finite.

Toric intersection conjecture. The toric variety $X(T)$ is the toric intersection of all the toric varieties $X(T_i)$.