11 problems

Degree-of-commutativity conjecture.

Finite-quotient formula conjecture.

Friedl–Löh conjecture. The uniform epimorphism problem onto the class of all finitely generated virtually abelian groups is not decidable.

For a group $G=\langle X\rangle$, let $[g]_c$ denote the conjugacy class of $g\in G$, and define the length up to conjugacy by … The strict conjugacy growth function is…

Bodart–Tashiro conjecture. The group $G$ is virtually Abelian if and only if it admits a Cayley metric whose metric-functional boundary is countable.

Let $G$ be an infinite group, and suppose that independent random-walk samples satisfy the law $x^2=1$ with positive probability. Leemann–de la Salle conjecture. If $G$ satisfies…

Let $G$ be a virtually abelian group, let $\mathcal S$ be a generating set, and write $\operatorname{Cog}_{\mathcal S}(t)$ for its cogrowth series. Virtually abelian cogrowth conje…

Undecidability conjecture. The uniform epimorphism problem onto the class of all finitely generated virtually Abelian groups is not decidable.

Let $G$ be a finitely generated virtually abelian group, and let $\operatorname{rank} G$ denote its rank. Write $\mathcal{D}_{G,S}^{lin}(n)$ for the linear sofic profile of $G$ rel…

Let $G$ be a finitely generated group, and let $X$ be a finite generating set. Define the degree of commutativity with respect to $X$ by … Here $\mathbb{B}_X(n)$ is the ball of rad…

Let $G$ be a group, let $\{\mu_n\}_{n\in \mathbb{N}}$ be a sequence of “reasonable” measures on $G$, and let $\mathcal{E}\subseteq F_k$ be a set of equations in $k$ variables. The…