6 problems

Benedetto–Ih conjecture. If $f_{d,\alpha}$ is not post-critically finite, then there are finitely many parameters $c\in\overline{K}$ that are $S$-integral relative to $(\alpha)$ an…

Let $f \colon {\mathbb{CP}}^n \to {\mathbb{CP}}^n$, with $n \ge 2$, be a post-critically finite endomorphism of degree $d \ge 2$, and let $\lambda$ be an eigenvalue of $f$ along a…

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 $f$…

Sparsity conjecture. Let $d\ge3$ and $n\ge2$. For every fixed tail-length $\ell\ge1$, the set

Relative rigidity conjecture. Every such family of post-critically finite maps is constant.

Let $f$ be the post-critically finite endomorphism of $\mathbb{P}\mathbb{C}^2$ considered above, with Julia set $J$. An orbispace metric is a metric on the orbifold-like space obta…