5 problems

Let an automaton group have degree $2$, meaning that every element $g$ has activity $a_n(g)=O(n^2)$, and let the associated degree-$2$ mother groups be the specific universal autom…

Let $G$ be a finite automaton group, and let $G_{\mathcal O}$ denote the orbit group associated with an orbit $\mathcal O$ of $G$. Orbit-group finiteness conjecture. For each finit…

Transience conjecture. The graph $\mathcal G(3,2,\infty)$ is transient.

Let $G$ be a polynomial automaton group of degree at most $2$, and let a random walk on $G$ have a step distribution with bounded support. The bounded-support zero-entropy conjectu…

Let $d$ be the degree of a mother group, and consider random walks whose step distribution is supported on a finite generating set. The mother-group zero-entropy conjecture. The mo…