9 problems

Let $\Sigma$ be a finite alphabet, and let a morphism on $\Sigma$ be called abelian power-free when its images avoid abelian powers of the relevant exponent. Carpi's set of condition…

The explicit limit conjecture for $L(2)$.

Let $L(w)$ denote the lexicographically least infinite word on $\mathbb{N}$ beginning with $w$ whose only square factors are contained in the prefix $w$. Let $L(\varepsilon)$ be th…

Antipalindromic fixed-point classification conjecture. The morphism $\varphi$ or its square $\varphi^2$ is conjugated to a morphism in

Let $T$ be the alphabet, and let an $n$-uniform squarefree morphism be a morphism $h:T^*\to T^*$ for which every image $h(a)$ has length $n$ and which maps squarefree words to squa…

Class $P'$ conjecture. There exists a morphism of class $P'$ such that its fixed point has the same language as ${\mathbf u}$.

Zero defect conjecture.

Let $X$ be a projective variety of dimension $n$, let $\pi:X\to Z$ be a surjective morphism of projective varieties of relative dimension $e$, and let…

Hof–Knill–Simon conjecture. ${\bf u}$ is palindromic if and only if there exists a morphism $\varphi\neq\operatorname{Id}$ such that