4 problems

Sturmfels–Sullivant's group-based degree-bound conjecture. For any group $G$, the ideal of the group-based model is generated in degree at most $|G|$ for any tree $T$.

Sturmfels–Sullivant's 3-Kimura conjecture. The ideal of the 3-Kimura model is generated in degree at most $4$ for any tree $T$.

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

Sturmfels–Sullivant's conjecture. For every abelian group $G$,