16 problems

Let $\mathcal{K}$ and $\overline{\mathcal{K}}$ be the two families of meromorphic modular forms in the source, and let $A_{\mathcal{K},k,m}(0)$ and…

Let $(A,S)$ be a Birkhoff interpolation scheme, with $S$ a lower set, and fix non-negative integers $p$ and $q$. An inverse shift moves elements of $A$ downwards and to the left wi…

Self-conjugate-grid uniform conjecture. For every $0\leqslant k\leqslant n-1$,

Schur-polynomial pointwise conjecture. For all $0\leq k<n\leq t$,

Self-conjugate-grid pointwise conjecture. For every $0\leqslant k\leqslant n-1$,

Let a $GC_n$ set be an $n$-correct set $\mathcal{X}$ in which the fundamental polynomial of every node is a product of $n$ linear factors. Gasca–Maeztu conjecture. Any $GC_n$ set c…

Strong Bergman asymptotics. The measures satisfy

Let $S_d$ be the real $d$-simplex, let $F_4$ be the set of $N=\binom{d+4}{4}$ points constructed in the paper, and let $\ell_j$ be the associated fundamental Lagrange polynomials.…

Let $S_d$ be the real $d$-simplex, let $F_4$ be the set of $N_4=\binom{d+4}{4}$ points constructed in the paper, and let $\ell_i$ be its fundamental Lagrange polynomials. The degre…

Let $H_{6,m}$ have Fourier expansion … where $q_m(z)=\exp(2\pi i z/\lambda_m)$ and $m\geq3$. Brent's $H_{6,m}$ interpolation conjecture. For every $n$, there is a polynomial…

Let $H_{4,m}$ have Fourier expansion … where $q_m(z)=\exp(2\pi i z/\lambda_m)$ and $m\geq3$. Brent's $H_{4,m}$ interpolation conjecture. For every $n$, there is a polynomial…

Let $X$ be a $GC_{d,n}$ set in ${\mathbb R}^d$, and call a hyperplane maximal when it contains ${d-1+n\choose n}$ points of $X$. de Boor's multiple-maximal-hyperplane conjecture. E…

Let $X$ be a $GC_{d,n}$ set in ${\mathbb R}^d$: it has ${n+d\choose d}$ points, and for every $p\in X$ there is a product of $n$ linear forms that equals $1$ at $p$ and $0$ at ever…

Conjecture concerning $GC_n$ sets. There is an integer $s$ with $2k-n-1\leq s\leq k$ such that

Positive-coefficient numerator conjecture. One can write

Let $X$ be a unimodular list of vectors, let $Z(X)$ be its zonotope, and let ${\cal Z}_-(X)$ be the set of integer points in the interior of $Z(X)$. Let $M_X$ be the box spline ass…