7 problems

Decidability equivalence. The following are equivalent:

Let $H_q$ be the Thue–Morse group, realized as the iterated monodromy group of the degree-$q$ branched covering described using the post-critical set…

Classification conjecture. $G$ is strongly hereditarily self-similar of index $p$ if and only if $G$ is isomorphic to

Let $G$ be a self-similar group and let $\mathcal{X}$ be its limit space. Let $W_t$ be Brownian motion on $\mathcal{X}$, let $d(0,W_t)$ denote its displacement from the base point,…

Let $G$ be a self-similar group as described in the source, and let ${\mathscr L}^\Bbbk(G)$ be its associated Lie algebra over the field $\Bbbk$. Let ${\mathscr L}(G)$ be the self-…

Let $G$ be a self-similar group as described in the source, let ${\mathscr A}(G)$ be its thinned algebra with augmentation ideal $\varpi$, and define its associated graded algebra…

Let $G$ be a group, and let its associated Lie algebra be defined from the relevant group-theoretic filtration. Torsion-group conjecture. If $G$ is a torsion group, then its associ…