5 problems

Twisted conjugacy growth series conjecture. The group $G$ is virtually abelian if and only if all its twisted conjugacy growth functions are rational. This is presented as a twiste…

Let $\Gamma$ be a virtually polycyclic group and let $\varphi:\Gamma\to\Gamma$ be an endomorphism. When the Reidemeister zeta function is well-defined, it is given by … where…

Let $\mathbf{B}$ be a Borel subgroup of a split, connected, reductive, non-commutative linear algebraic group $\mathbf{G}$, all defined over a global field. An $S$-arithmetic subgr…

Twisted conjugacy separability domination conjecture. For every automorphism $\varphi\in\operatorname{Aut}(N)$,

Let $G$ be a group, let $\operatorname{Aut}(G)$ denote its automorphism group, and for $\varphi\in\operatorname{Aut}(G)$ let $[e]_{\varphi}$ be the twisted conjugacy class of the i…