9 problems

Full-shift noncommutativity conjecture. The full vector shift $X$ is not compatible with a nontrivial Lie algebraic subshift structure.

Let $X$ be a subshift, meaning a closed, shift-invariant subset of $A^{\mathbb{Z}}$ for a finite set $A$. For each $n$, let $F_X(n)$ be the set of distinct follower sets of words o…

Let $\Xi$ be a minimal, aperiodic and uniquely ergodic ${\mathbb Z}^2$ subshift, and let $\Omega$ be its suspension. Let $\lambda=(\lambda_x,\lambda_y)$ be a virtual eigenvalue of…

Let $\mathcal{A}\subset \mathbb{R}$ be finite, and let $\Omega\subset \mathcal{A}^{\mathbb{Z}}$ be a minimal subshift that is not periodic. By minimality, the Schrödinger operators…

Let $\mathcal{A}$ be a finite alphabet of Verblunsky coefficients, and let $\Omega\subset \mathcal{A}^{\mathbb{Z}}$ be a minimal subshift that is not periodic. The associated measu…

Let $X$ be a countable quasiminimal recursive subshift. The model-checking problem asks whether the language of $X$ intersects a given formal language. Locally testable decidabilit…

A universal symbolic system is a symbolic dynamical system capable of simulating every effective symbolic system. Universality conjecture. Every universal symbolic system has infin…

Fix a finite alphabet $S$. For a subshift $X\subset S^\mathbb{X}$, let $h(X)$ denote its topological entropy and let $W(X)$ denote its winning shift. High-entropy winning-shift con…

Weak conjugacy conjecture. The limit set of any stable cellular automaton is weakly conjugate to an SFT.