Open Collections

Description

Let G be an algebraic group over an algebraically closed field. A subset S of G topologically generates G if the subgroup generated by S is dense in G, with respect to the Zariski topology. In this talk, I will report on recent work with Spencer Gerhardt and Bob Guralnick on the topological generation of simple algebraic groups by elements in specified conjugacy classes. I will explain some of the main ideas and I will present new results for exceptional algebraic groups. I will also describe an application concerning the random generation of finite simple groups of Lie type.