5 problems

Let ${\cal G}$ be an $\mathbb R$-rational building set. A real subspace $C\in{\cal C}_{\cal G}$ is purely complex when it decomposes as … Write $\mathbb R({\cal G})$ for the real s…

Let $Y_V \subset \mathbb{P}^{\mathbf n}$ be a Schubert variety of a subspace arrangement, and write its Chow class as … For a basis $\mathbf b=(b_1,\ldots,b_N)$, Chow-class coeffic…

Let $s$ be a positive integer and let $b$ be a complex parameter. For the partition … let $Y_\lambda$ denote the associated quotient arrangement. Generic Cohen–Macaulayness conject…

Let $b>c$ and let $q,r,s$ be positive integers. For the partition … let $X_\lambda$ denote the associated subspace arrangement. Three-part non-Cohen–Macaulayness conjecture. If…

Let $W$ be a finite real reflection group, and let $\mathscr{P}$ be a collection of rank $2$ parabolic subgroups of $W$ closed under conjugation. Set … Define a Coxeter group $W'$…