3 problems

Let $q$ be a prime number, let $S$ be a random subset of $\textit{GL}_k(\mathbb{Z}_q)$, and let $G_k$ be the Schreier graph of $S \subset \textit{GL}_k(\mathbb{F}_q)$ acting on…

Decidability equivalence. The following are equivalent:

Bellaterra expander conjecture. The Bellaterra graphs $\{B_i\}_{i=1}^\infty$ are a family of two-sided expanders. The authors' computations suggest an eigenvalue gap of roughly…