4 problems

Let $\Phi$ be a finite crystallographic root system of rank $n$, and let $m$ be a positive integer. The generalized cluster complex $\Delta^m(\Phi)$ is the simplicial complex assoc…

Let $G$ be a complex reductive group with Borel subgroup $B$, Weyl group $W$, and let $X_w=\overline{BwB/B}$ be the Schubert variety associated with $w\in W$. For $I\subseteq J(w)$…

Generalized cluster complex conjecture. Every generalized cluster complex $\mathcal C(m,\Phi)$ is pure-EKR.

Simpliciality conjecture. The fan $\operatorname{biCamb}(W,c)$ is simplicial. Equivalently, its dual polytope is simple.