12 problems

Let $K$ be a compact connected Lie group with normalized Haar measure $dg$, and let $f$ and $g$ be complex-valued $K$-finite functions. Mathieu's conjecture. If … then … for all su…

The XZ conjecture for $G_2$. If

Let $N\geq 2$, and let $f:[0,1]^{\frac{N(N-1)}{2}}\times \mathbb{T}^{\frac{N(N+1)}{2}-1}\to\mathbb{C}$ be an admissible function, meaning that it has a finite expansion in the toru…

Weighted Laurent-polynomial spectrum conjecture. If

Weighted Laurent-polynomial Mathieu conjecture. If

Let $S^*$ denote the unit circle, and let $\tilde J_{G_2}$ be the weight function associated with the paper's Euler-angle parametrization of $G_2$. A function … is $\frac{1}{4}$-ad…

Let $N\in\mathbb{N}$, and let $S^*$ denote the unit circle. A function … is $\frac{1}{N}$-admissible if it is a finite sum $\sum_{\vec m}c_{\vec m}(x)z^{\vec m}$, where the exponen…

Let $N\geq 2$, set $k=\frac{N(N-1)}{2}$ and $l=\frac{N(N+1)}{2}-1$, and let $S^*$ denote the relevant multiplicative parameter space. A $SU(N)$-admissible function is a function ……

Let $h$ be an admissible function on $\mathbb{T}^k\times[0,1]^l$ of the form … where $\mathbf m=(m_1,\ldots,m_k)$ is an integer multi-index, each $c_{\mathbf m}$ is a complex polyn…

Let $f=\sum_{i=1}^{k}A_i t^{\ell_i}_{m_i,n_i}$ be an $SU(2)$-finite function, with $A_i\neq0$ for every $1\leq i\leq k$. Let $C$ be the closed convex hull of the points…

Let $u_1,\ldots,u_n$ be coordinates on $(0,\infty)^n$, and let $f\in\mathbb C[u_1,\ldots,u_n]$. Put $B=(0,\infty)^n$. Exponential integral vanishing conjecture. If … for almost all…

Zhao's integral conjecture. The subspace $M$ is a Mathieu subspace of $\mathbb C[x]$. The conjecture is widely open in all dimensions and implies the Image Conjecture for classical…