7 problems

Let $\mathcal{A}$ be the tuple of supports defining a sparse resultant, let $\mathcal{H}_{\mathcal{A},\rho}$ be the Canny–Emiris matrix whose rows encode the coefficients of the po…

Equality conjecture. The inequality above is an equality. Equality is already known in the cases $k=1$, $k=n-2$, and $k=n-1$; the conjecture asserts equality for every…

Minimum-dimension box-center conjecture. If the data $\boldsymbol l,\boldsymbol d,\boldsymbol s$ are determinantal, then determinantal degree vectors of minimum matrix dimension li…

Multigroup center conjecture. For $r>1$, a similar explicit choice of a minimum-dimension formula exists, namely one obtained from the centers of the relevant determinantal boxes.

Box-center conjecture. Minimum-dimension formulae appear near the centers of these boxes.

Center conjecture. A formula of minimum dimension should be recoverable from the centers of the determinantal boxes, analogously to the homogeneous case.

Let $x$ be the spectral-curve coordinate and let $\widetilde{K}(z_1,z_2)$ be the formal Baker–Akhiezer kernel defined by … where the primed sum excludes all terms with…