6 problems

The conjecture. If $u\in\mathcal G(\mathbb R^d)$ is weakly homogeneous of degree $\alpha$, then there is a representative $(u_\varepsilon)_\varepsilon$ of $u$ such that, for every…

Let $x\in R^n$ and $t\in R^r$, let $\Omega\subseteq R^r$ be open, and consider distribution solutions of the functional equation (1.1) satisfying assumptions A-1 through A-5. Let…

Let $\pi:S[\{0,1\}]\to\mathbb{Z}_{\geq0}$ interpret a binary word as an integer, and let $u_1<u_2<\ldots<u_{k_n}$ be the ordered elements of $\pi(\mathscr{U}_n)$. Define … Let…

Let $f(x)$ be a polynomial of degree $n$. For a prime $p$ in $Spl(f)$, number the roots of $f(x)$ modulo $p$ as … For a subset $S\subseteq\{1,2,\dots,n\}$, write $Pr(f,S)$ for the…

Let $H$ be a distribution with co-rank $s$ and rank $r$, so that its derived distribution satisfies $[H,H]=T$ and hence $s<r(r-1)/2$. Square-root growth conjecture. The minimal pos…

Nonexistence conjecture. There exists $u\in{\rm Gen}_{\mathscr{S}}(\mathbb{R}^d)$ such that