6 problems

Generating conjecture. The ideal of homogeneous invariants for the 2-state GM+I model on $T$ is generated by those $3\times 3$ minors of edge flattenings that do not involve the va…

Klein four-group phylogenetic complexity conjecture. The phylogenetic complexity of the group $G=\mathbb{Z}_2\times\mathbb{Z}_2$ is four:

Finite abelian group bound. For any finite abelian group $G$ and any positive integer $n$,

Garcia–Stillman–Sturmfels conjecture. The ideal $\mathfrak a(2;2,2,\dots,2)$ is generated by the $3\times 3$ minors of all two-dimensional flattenings arising from bipartitions of…

Vertex-flattening generation conjecture. For any $\kappa$ and any number of taxa $n$, the phylogenetic ideal $\mathfrak a_T$ for the general Markov model on a binary $n$-taxon tree…

Let $T$ be a phylogenetic tree, let $G\leq \mathcal{S}_{\kappa}$ be a permutation group, let $V_T$ be the variety associated to $T$ under the general Markov model, and let…