14 problems

Point-spectrum conjecture. One has $\alpha\in\sigma_p(\widetilde A)$ if and only if either there exists a nontrivial element $y_0$ such that

Let $K=\mathbb{F}_q(t)$ be a rational function field and let $v$ be a finite monic prime. Write $W_v(K)$ for the vector space of $v$-adic multiple zeta values at integer tuples. Od…

Let $K=\mathbb{F}_q(t)$, and let $W(K)$ be the product over monic primes $v$ of the vector spaces $W_v(K)$ spanned over the relevant coefficient field by the $v$-adic multiple zeta…

Let $\mathcal{B}$ be the indexing set of compositions used for the double-tail multiple zeta values, let ${\bf Z}^{(\mathcal{B})}$ be the corresponding free abelian group, and let…

M. Stein's conjecture. One has $\dim_{\mathbb{Q}}V_m=m$ for every positive integer $m$. Moreover, for every $\left(t_1,\ldots,t_{4m}\right)\in V_m$,

Let $\bold{Mark}$ and $\bold{LinRel}$ be the symmetric monoidal bicategories whose objects are finite sets, whose morphisms are open Markov processes and linear relations respectiv…

Let $\bold{Mark}$ and $\bold{LinRel}$ be the symmetric monoidal bicategories obtained from the symmetric monoidal double categories $\mathbb{M}\mathbf{ark}$ and…

Let $f$ be an odd-degree polynomial of degree $D$, and let $\varphi_{D,0,\rho}$ denote the quantities used in the source for indices $D$, $0$, and $\rho$. Odd-degree peculiar linea…

Let a collection consist of mono- or bi-brackets, viewed as elements of the relevant bracket algebra over $\mathbb Q$ and $\mathbb C(q)$. Rationality conjecture for bracket relatio…

Let $[s_1,s_2,s_3]$ denote a bracket of weight $s_1+s_2+s_3$ and length three in the multiple-divisor-sum algebra $\operatorname{\mathcal{MD}}$. Length-three bracket relations. In…

Let $k\geq 4$. Consider the linear relations among the generators of the weight-$k$, length-two component…

Standard-level sharpness conjecture. If $N$ is a standard level, the standard relations always give the sharp bound for $d(w,N)$; equivalently, all linear relations derive from the…

Sharp-bound conjecture for levels 8, 10 and 12. The bounds $D(w,N)$ are sharp in these cases, and the following relations are the non-standard ones:

Non-standard-relation conjecture. Non-standard relations do not exist; equivalently, $SR(N)$ is sharp. The source reports verification only for the first two prime squares, $N=25$…