7 problems

Klein four-group phylogenetic complexity conjecture. The phylogenetic complexity of $G$ is

Eventual constancy recurrence.

The $K_{1,3}$ conjecture.

Let $T$ be a binary tree, let $\mathcal{M}_T$ be its general Markov model, and consider the rank varieties described in (1) and (2): the varieties defined by the rank conditions on…

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

Prolongation intersection conjecture.

Claw-tree intersection conjecture. The varieties associated with large claw trees are scheme-theoretic intersections of varieties associated with trees of smaller valency.