8 problems

Let $\mathbf{w}_1,\ldots,\mathbf{w}_{n+1}\in\mathbb{R}^n$ be the vectors of a regular simplex frame, and let … be the associated symmetric tensor of order $m$ and dimension $n$, wh…

Let $X^*=\\{x_1,x_2,x_3,x_4,x_5\\}$ be an optimal configuration for the projective Riesz-kernel problem with parameter $s\in[0,\infty)$ and $N=5$, where the points $x_i$ lie on the…

Let $d$ be the dimension of a SIC, and consider the structures associated to it that are constructed in the paper. Continuous-family conjecture. Such families exist for every integ…

Let $d$ be the dimension of a SIC, and consider the projector, complex Hadamard matrix, equiangular tight frame, and, where applicable, tight fusion frame structures constructed fr…

Semi-regular Dubuc–Deslauriers wavelet frame conjecture. The matrix $\mathbf{R}_{irr}$ is positive semidefinite, and, for every $\alpha\in\{0,\dots,n-1\}$, the bi-infinite vectors…

Cross-polytope projection volume conjecture. The upper bound for the volume of such a projection is

Single-generator continuity conjecture. There is no affine shear tight frame with one single generator that is continuous.

Distributional-limit conjecture. The distribution result of Theorem continues to hold with $M$ replaced by $n$.