6 problems

Normal-form conjecture. In the second form, $u$ and $v$ satisfy restriction (a); in the third form, they satisfy restriction (b); and in the fourth form, they satisfy both restrict…

Let $M_4 = \operatorname{Mon}\langle a,b\mid aba^2=ba\rangle$ and let $M_7$ denote its anti-isomorphic one-relation monoid. A faithful tropical representation of a monoid is an inj…

Let $M_5 = \operatorname{Mon}\langle a,b\mid aba=ba\rangle$ be the one-relation monoid with defining relation $aba=ba$. Its UT-rank is the least $n$ such that $M_5$ admits a faithf…

Non-finite generation conjecture. If $M$ is a non-zero CQP monoid, then $M$ is not finitely generated as a monoid.

Let $M$ be a positive homogeneously presented cancellative tame monoid whose idealistic subsemigroup is finitely generated. Solvability conjecture. The conjugacy problem in $M$ is…

Weak left-Garside conjecture. The monoid $A_n$ is a weak kind of left-Garside monoid.