let $\omega\subseteq {\rm gl}_n(f_p(t))$ be a finite symmetric set containing the identity. let $\gamma$ be the group generated by $\omega$ and let $\mathbb{g}$ be the zariski-closure of $\gamma$. we discuss conditions on which the family of cayley graphs $\{{\rm cay}(\gamma ({\rm mod} q), \omega)\}$ is a family of cayley graphs as $q$ ranges through a certain subset $\sigma$ of $f_p[t]$. this problem is a positive characteristic variation of the work of bourgain-gamburd, varju, salehi golsefidy-varju, and others. we focus on the difficulties that arise in positive characteristic. please note: there will be pre-talk for graduate 2022年亚洲世界杯预选赛 from 2:30 - 3:00. the regular talk will begin at 3:00.