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Topological generation of algebraic groups

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Group theory and generalizations; Geometry; Algebraic structures

video/mp4

Author affiliation: University of Bristol

2020-02-24

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73586

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/