CSUN Algebra, Number Theory, and Discrete Mathematics Seminar

Let $G$ be a classical algebraic group over an uncountable algebraically closed field, and let $C_1,\dots ,C_e$ be conjugacy classes of $G$. In this talk, we consider the following question: when do there exist elements $g_1,\dots ,g_e\in C_1,\dots ,C_e$ such that $⟨g_1,\dots ,g_e⟩$ is Zariski dense in $G$? We will discuss results for ${\mathrm{SL}}_n\left(k\right)$, and consider some connections to random generation problems for finite simple groups of Lie type.