5 problems

Let $G$ be a group acting by type-preserving simplicial isometries on a building $\Delta$. Let $X$ be the Davis realization of $\Delta$, and call the action locally elliptic if every…

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

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…