8 problems

Let $A$ be an integer matrix, let $\mathcal{M}_A(\beta)$ be the projectivized $A$-hypergeometric system with parameter $\beta$, and let $Y$ be a coordinate variety. For a filtratio…

Let $A$ be fixed, let $L$ be a filtration, let $\tau$ be the corresponding face or stratum, and let $\mu^{L,\tau}_{A,0}(\beta)$ denote the multiplicity of the associated component…

Let $A$ be an integer matrix, let $S_A$ be its semigroup ring, and let $\mathfrak m$ be its homogeneous maximal ideal. For each $i<\dim(S_A)$, let $H^i_{\mathfrak m}(S_A)$ denote t…

Consequences conjecture. For generic choices of $u\in\mathbb{C}^{n+1}$:

Integral representation conjecture. For generic choices of $u\in\mathbb{C}^{n+1}$, the morphism $\psi$ is an isomorphism of $D_Z$-modules.

Covering conjecture. On each member of this open covering, the system $E(n,m)$ is represented locally by a $GKZ$ system; equivalently, the hypergeometric $\mathcal{D}$-modules of…

Let … and … Define the Wronskian … and let $F=W\circ\lambda$, where … for $q$ in the punctured unit disc $\Delta^*=\{q\in\mathbb C:0<|q|<1\}$. Wronskian nonvanishing conjecture. Th…

Let $C$ be a rational polyhedral cone in a lattice $N$, let $C^\circ$ denote the associated dual data, and let $bbGKZ(C,0)$ and $bbGKZ(C^\circ,0)$ be the corresponding better-behav…