6 problems

Let $K$ be a finite extension of $\mathbb{Q}$ or $\mathbb{F}_p(t)$, where $p$ is prime. For integers $d\geq 2$, define $K\in\mathcal{N}_{d,n}^{\infty}$ to mean that $K$ admits the…

For a field $K$, let $K\in\mathcal{N}_{d,n}^{\infty}$ mean that there exists a degree-$d$ polynomial over $K$ whose first $n$ iterates, and all further iterates, remain irreducible…

Let $p$ be a prime, let ${\mathbb F}_p$ be the finite field with $p$ elements, and let $f(x)\in{\mathbb F}_p[x]$ be a polynomial whose degree is divisible by $p$. A polynomial over…

Let $K$ be a field of characteristic different from $2$, and let $f(x)\in K[x]$ be a monic, post-critically finite quadratic polynomial. Let $o_f$ denote the period of the post-cri…

Let $S$ be the set given in Proposition 3.8. For $m\in S$, define … Stability conjecture. For every $m\in S$, the polynomial $f$ is stable, meaning that every iterate $f^n$ is irre…

Let $\overline{f}$ denote the reduction of a polynomial $f$ modulo a prime. Odoni–Stoll conjecture. For … $\overline{f}$ is stable for $p=3$ and for no other primes. Odoni observed…