10 problems

Degree-eight distinct-diagonal test case. Every reducible connected degree-eight spectral curve is obtained from a constant branch or from reversal symmetry. In particular, there i…

Amended reducibility conjecture. Every reducible factorization of $\chi_n$ is expected to be obtained by iterating the following operations on connected blocks: cutting the chain a…

Let $\rho$ and $\beta$ be c.a. reals, where $\rho$ is Solovay reducible to $\beta$ in the S2a sense, denoted $\rho{{\le}_{\mathrm{S}}^{\mathrm{2a}}}\beta$. Generalized Limit Theore…

Let $X,Y\subseteq\omega$, and let $\mathcal{G}^X$ and $\mathcal{G}^Y$ be the generalized computability models defined in the paper. An embedding $f:\mathcal{G}^X\to\mathcal{G}^Y$ i…

Strong nonvanishing conjecture. The operator $M^*(s,\rho_c(\tau_a)\otimes \rho_d(\tau_b))$ is nonzero for every $s\in\mathbb{C}$.

Let $G$ be a reductive group, let $P=MN$ be a parabolic subgroup, and let $I^G_P(\sigma)$ be the parabolic induction of an irreducible admissible representation $\sigma$ of $M$. Su…

McDiarmid–Reed reducibility conjecture. For every hexagonal graph $G$, $\operatorname{core}_{\mathcal{F}_{9,4}\cup\mathcal{F}'_{9,4}}(G)$ is $(9,4)$-colorable.

Squarefreeness conjecture. The polynomial $F_{m,n}$ has no multiple roots.

A trellis represents a code, and a trellis is nonminimal when it is not minimal for that code. A reduction procedure consists of the reduction steps from the proof of Theorem; stat…

Three-linear-factor conjecture. There are no trinomials $x^n+A x+B$ defined over $\mathbb{Q}$ with reducibility type $(1,1,1,n-3)$.