8 problems

Subdivision conjecture. The moment polyhedron $\Phi_T(G/B)$ has a locally finite subdivision into Bruhat interval polytopes

Let $\mathring{\mathcal{B}}_{v,w}$ be an open Richardson variety in a symmetrizable Kac--Moody setting, and let $\mathbb{C}[\mathring{\mathcal{B}}_{v,w}]$ carry the natural upper c…

Let $W$ be the Weyl group of a Kac–Moody group, let $v,w\in W$ satisfy $v\leq w$, and let $\textnormal{\textbf{w}}$ be a reduced expression for $w$. Denote by…

Let $G$ be a Kac–Moody group, let $w$ be an element of its Weyl group, and let $N(w)$ be the associated unipotent subgroup. The coordinate ring $4[N(w)]$ has a cluster algebra stru…

Let $W_{\mathcal{T}}$ be the double-affine Weyl monoid, let $\widetilde{\Delta}^+$ denote the positive double-affine real roots, and let $\ell$ be the length function. Deodhar's in…

Let $W_{\mathcal{T}}$ be the double-affine Weyl monoid, equipped with its Bruhat order $<$ and length function $\ell$. Write $x\lhd y$ when $y$ covers $x$, meaning that $x<y$ and t…

Choose a marking of each conjugacy class $\breve{\mathcal{C}}_i\subset \operatorname{GL}(V_i)$ for all $i\in I$. Gluing legs to obtain a supernova graph $\widehat{\Gamma}$ with nod…

A Kac-Moody symmetric space is a symmetric space associated with a Kac-Moody group or algebra. A moduli space parametrizes geometric objects of a specified type up to the relevant…