10 problems

Takayama's conjecture. The holonomic dual of an $A$-hypergeometric system is itself a GKZ system.

Let $A\subset\mathbb{Z}^d$ be a configuration. Its sparse discriminant is denoted by $D_A$. The configuration is GKZ-rational if $D_A$ is not a monomial and there exists a nonzero…

Let $Y_{\mathrm{nc}}$ be a non-commutative resolution constructed above under the gauge-fixing assumptions, and let $X$ be a Calabi–Yau complete intersection with $\dim(X)=\dim(Y)$…

Restricted GKZ singular-locus conjecture. The singular locus of a restricted GKZ system arising from a Feynman integral coincides with the Euler discriminant.

In the setup above, let the solutions of $\mathrm{bbGKZ}(C,0)$ and $\mathrm{bbGKZ}(C^\circ,0)$ be identified, in suitable regions of the parameter space, with cohomology or $K$-the…

Let $C$ be a finite rational polyhedral cone in a lattice $N$, with degree-one lattice points $v_1,\ldots,v_n$ as above. Let $\mathrm{bbGKZ}(C,0)$ and $\mathrm{bbGKZ}(C^\circ,0)$ d…

Let an irregular GKZ system be associated with a Newton polytope, and let a facet of that polytope be a codimension-one face that does not contain the origin. Fang–Feng conjecture.…

Let $X_{\underline{t}}$ be the family of anticanonical hypersurfaces associated with the polytope $\Delta$, let $\nabla$ be its Gauss–Manin connection, and let…

Borisov–Horja duality conjecture. There exists a collection of polynomials $p_{c,d}(x_1,\ldots,x_n)$, indexed by $c\in C$ and $d\in C^{\circ}$, such that only finitely many are non…

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…