18 problems

Let $G$ be a finitely generated amenable group. Its integral group ring is denoted by $\mathbb{Z}G$. A group ring is properly coherent when it is coherent but not Noetherian. A pro…

Higher-dimensional coherence conjecture. Any small lax $n$-category is laxly $n$-equivalent to a small Gray $n$-category.

Surface-by-cyclic group-algebra coherence conjecture. The group algebra $\mathbb{Q}[G]$ is coherent. The source identifies the virtual surface-group case as difficult and open, mot…

Let $G$ be a RFRS group of type $\mathrm{FP}$. A group is coherent if every finitely generated subgroup is finitely presented. The algebra $\mathbb{Q}[G]$ is the rational group alg…

Coherence conjecture. All such maps defined as composites of associators, unitors, and interchange morphisms are equal.

Non-coherence conjecture. For all $0 \leq m \leq n-1$, $G$ is not $m$-coherent.

Let $X$ be an aspherical two-complex and let $G=\pi_1(X)$ be its fundamental group. Say that $G$ has trivial second $L^2$-Betti number when $b_2^{(2)}(G)=0$. Betti coherence conjec…

Non-positive irreducible curvature implies coherence. If $\rho_+(X)\leq 0$ then $\pi_1(X)$ is coherent.

Let $F$ be a frame for $\mathbb{F}^n$, and let $G$ be one of its dual frames. Write $Gr(F,G)$ for their cross Gramian and let $\mu(Gr(F,G))$ denote its maximum off-diagonal magnitu…

Let $\mathcal{C}$ be a braided semigroupal polyadic category with an $n$-ary tensor product, an $n$-ary associator $\scalebox{1.15}{\textsf{\upshape A}}^{\left(2n-1\right)\otimes}$…

$n$-ary coherence conjecture. If the $n$-ary associator $\scalebox{1.15}{\textsf{\upshape A}}^{\left(2n-1\right)\otimes}$ satisfies such $n$-ary coherence conditions that this isom…

Let $G=F_m\rtimes F_n$ be a semidirect product of free groups, where $m,n\geq 2$. A group is incoherent if it has a finitely generated subgroup that is not finitely presented. Wise…

Wise's conjecture. The fundamental group $\pi_1X$ is coherent.

$l_1$-coherence dominance conjecture. For all states $\rho$,

Let $G$ be a Coxeter group with standard $2$-complex $X$, and let $\overline X$ be the compression of a finite cover of $X$ corresponding to a finite-index torsion-free subgroup. S…

Let $G$ be a finitely generated infinite Coxeter group of dimension at most $2$. Its Euler characteristic is denoted by $4\chi(G)4$. Positive Euler characteristic conjecture. If ……

Let a spacial traced category be a planar traced category satisfying the spacial and spherical axioms, and consider the graphical language in which diagrams are identified up to is…

Let a planar traced category be a monoidal category equipped with right and left traces satisfying the three additional axioms of interchange, left pivoting, and right pivoting, an…