7 problems

Invariant-cone conjecture. Every irreducible Perron semigroup has an invariant cone.

Consider the decision problem of determining whether a finitely generated matrix semigroup is finite. The paper gives a $\operatorname{coNEXP}^{\operatorname{NP}}$ upper bound for…

Let $\mathcal{M}$ be a finite set of $m$ rational $n\times n$ matrices, and let $\overline{\mathcal{M}}$ be the finite multiplicative semigroup generated by $\mathcal{M}$. The pape…

Generalised regularity classification. The displayed classification summarises the generalised regularity properties of $M_n(\mathfrak{L})$, $UT_n(\mathfrak{L})$, and…

Let $\mathbb{T}$ denote the tropical semifield, let $UT_2(\mathbb{T})$ be the monoid of all $2\times 2$ upper triangular matrices over $\mathbb{T}$, and let $\mathcal{B}$ be the bi…

Let $M_n(\mathbb{T})$ denote the monoid of $n\times n$ tropical matrices, where $n$ is a positive integer. Izhakian–Margolis conjecture. The monoid $M_n(\mathbb{T})$ satisfies an i…

Let … and let $\langle R,S\rangle$ be the semigroup generated by these matrices. Integer-eigenvalue conjecture. The only matrices in $\langle R,S\rangle$ that have integer eigenval…