5 problems

Let $f\in \mathbb{C}[x]$ be a post-critically finite rational function. Write $\mathrm{IMG}(f)$ for its iterated monodromy group, and say that it has $(\mathrm{LR})$ when it has th…

Let $f: \mathbb{C}^n \to \mathbb{C}^n$ be post-critically finite. An affine Weyl iterated-monodromy characterization conjecture asserts that if the iterated monodromy group of $f$…

Let $f(x)\in\mathbb{Q}[x]$ be a quadratic polynomial, let $\alpha\in\mathbb{Q}$, let $T$ be the binary tree, and let … be the associated arboreal representation. An element of its…

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…

Let $P$ be a postcritically-finite non-renormalizable quadratic polynomial whose Julia set $\mathcal{J}_P$ is a dendrite. Intermediate-growth conjecture. The iterated monodromy gro…