86 problems

Demailly's conjecture. The inequality

Equivalence conjecture. The quantity $R_T$ defined by equation (def-RT) and the projected circumradius of $T$ are equivalent.

Higher-order equivalent-norm conjecture. The two displayed equivalent-norm estimates should also hold for every $r\geq 3$.

Non-algebraic perp conjecture. If $a_n,c_n>0$ are chosen as above, then

Non-semi-algebraic unit-ball conjecture. The unit ball determined by the constructed $3$-idempotent operator algebra is not a semi-algebraic set.

Non-semi-algebraic interpolation-body conjecture. For a sufficiently pathological uniform algebra, there will exist interpolation bodies that are not semi-algebraic.

Projection conjecture. At most $k(n-1)$ points of $\phi_4(\Sigma)$ can be contained in a curve of degree $k$ in $\mathbb{P}^2$.

Let $D\subset\mathbb{N}^{2}$ be finite, and consider a system $\mathcal{L}_{D}(m_{1},\dots,m_{r})$. The system admits a reduction algorithm if there is a sequence of sets … that sa…

Interpolation conjecture. For every derivation $T\vdash_{\mathsf{SKS}}R$, there is a structure $P$ and derivations

Let $w_n$ be given by equation $(15)$, let ${\mathcal H}_{\mathbf w}$ be the corresponding Hilbert space, and let $Mult({\mathcal H}_{\mathbf w})$ denote its multiplier algebra. A…

Reformulated generalised Harbourne–Hirschowitz conjecture. The class $H$ is non-special and separates $k$-clusters if

Generalised Harbourne–Hirschowitz conjecture. Let $k\geq 0$ be an integer. If $H$ is an effective divisor class on $X_r$ with

Even-degree parameter-set conjecture. For all $k\in\mathbb{N}$, there exist constants $c_{2k}$ such that

Asymptotic interpolation conjecture. If $k\geqslant3$ and

Yin and Wu's size interpolation conjecture. If

$(Q_n)$ conjecture. $(Q_n)$ is true for all nonnegative integers $n$.

Let $f_n(x)$ be the Fourier interpolation basis functions. Logarithmic square-norm conjecture. For $n>1$, one has … The lower bound is already known from the result cited in the pa…

Let $f_n(x)$ be the Fourier interpolation basis functions, and let $\varepsilon,\delta>0$. Consider the region $\varepsilon n\le x\le n-\sqrt n$. Interior-region decay conjecture.…

Let $f_n(x)$ denote the basis functions of the Fourier interpolation considered in the paper, for $n\in\mathbb{Z}_{\ge0}$ and $x\ge0$. Uniform boundedness conjecture. There exists…

Let $(T,U)$ be fixed, let $\MatsubaraFrequencyCutoff$ denote the Matsubara-frequency cutoff, and let $\HybridizationVector$ and $\mathbf{G}$ be the quantities appearing in the disc…

Let $MP_n$ be the Morrow-Patterson points for positive integer $n$, and let $\Lambda_n^{MP}$ denote the corresponding Lebesgue constant. Interpolation at $MP_n$ can be interpreted…

d'Horace conjecture. The méthode d'Horace, or a simple modification of it, applies in weighted projective space.

Entailment-to-interpolant-existence conjecture. The IEP for $L$ is decidable whenever entailment in $L$ is decidable.

Let the interpolant existence problem (IEP) ask whether, for a given pair of formulas in a logic, there is an interpolant between them. A Priorean temporal logic is a temporal logi…

Consider the radially symmetric setting studied for the network interpolation problem, and let a minimum norm interpolant be a function that fits the prescribed data while minimizi…