5 problems

For each integer $n\geq 1$, let $\mathrm{Per}_n(0)\subset \mathrm{M}_2$ be the PCF-special curve parametrizing quadratic rational maps for which one critical point has exact period…

Let $f(x)=1/(x-1)^2$, and let $G_n^{\mathrm{geom}}(f)$ denote its geometric iterated monodromy group at level $n$. Conjecture 7.15. For the relevant levels $n$, one has … This conj…

Ih–Rees–Silverman conjecture. When $k\geq2$, the PCF endomorphisms are not Zariski dense in the space $\operatorname{End}_d^k$ of all degree-$d$ endomorphisms of $\mathbb{P}^k$.

Global curve attractor conjecture. Every postcritically-finite rational map with a hyperbolic orbifold has a finite global curve attractor.

Let $X$ be a smooth, irreducible, projective variety defined over the field of fractions $K$ of a Dedekind domain $R$. Let $\varphi:X\to X$ be a morphism defined over $K$, let…