6 problems

Majority Dynamics conjecture. For every $\varepsilon>0$, with high probability the number of oscillating vertices lies in

Let $G$ be a locally cyclic graph with boundary and minimum degree $\delta\ge 4$ triangulating a disc. Such a graph is clique null if its clique dynamics converges to the one-verte…

Let $G$ be a locally cyclic graph of minimum degree $\delta\ge 4$ triangulating a closed surface of Euler characteristic $\chi\ge 0$; equivalently, the surface is a sphere, project…

Antimorphic-digraph tau-sequence conjecture. The $R$-systems associated with antimorphic digraphs possess strong $\tau$-sequences $Y(t)$ with the substitution

Let $\Gamma_n$ be the graph considered in the paper, and let $\mathcal{S}_n^\star$ be the distinguished update system supported on $\Gamma_n$, with preferred state $\star$. A point…

Let $\Gamma$ be a finite directed acyclic graph. Its universal dynamics monoid $D(\Gamma)$ is the smallest quotient of $\operatorname{\mathbf{HK}}_\Gamma$ through which all evaluat…