10 problems

Nearly symmetric word conjecture. A word has positive trace for every pair of positive definite letters if and only if the word is nearly symmetric.

Let $M$ be a monoid and let $\phi:M\to M$ be an endomorphism. The Bruck–Reilly extension $\operatorname{BR}(M,\phi)$ is the monoid constructed from this data. A monoid is…

Let a finitely generated strong semilattice consist of finitely generated semigroups whose connecting morphisms respect the semilattice structure. A semigroup is $U(\mathcal{DCF})$…

Let $\operatorname{FIM}_1$ be the free inverse monoid of rank $1$. Write $\operatorname{WP}(\operatorname{FIM}_1)$ and $\iota(\operatorname{FIM}_1)$ for its two word problem langua…

Let $\operatorname{FIM}_k$ be the free inverse monoid of rank $k$, and let $\operatorname{WP}(\operatorname{FIM}_k)$ and $\iota(\operatorname{FIM}_k)$ denote its two word problem l…

Let a finitely generated group have a $\Pi^0_1$ word problem, meaning that its word problem is a co-c.e. equivalence relation on words, but suppose it is not isomorphic to a finite…

Brough's conjecture. The classes $\mathcal{PG}$ and $\mathcal{D}$ coincide.

Let $(\mathcal{S},\mathcal{R})$ be an Artin–Tits presentation, and let denote the reducing equivalence defined earlier in the paper. Reducing conjecture. Every Artin–Tits presentat…

Let $M$ be the monoid with the flag braid presentation … and let $B_4$ be Artin's braid group with standard generators $\sigma_1,\sigma_2,\sigma_3$. Flag braid embedding conjecture…

Let $B_n$ be the braid group with generating set $\Sigma=\{\sigma_1,\ldots,\sigma_{n-1}\}$, and let $l_\Sigma(w)$ denote the $\Sigma$-length of a braid $w$. A braid word is…