Varieties and Pro-Lie Groups: Connected vs Disconnected

Varieties of Topological Groups were introduced by the speaker almost 50 years ago and Pro-Lie Groups were introduced by Karl Heinrich Hofmann and the speaker early this century. This seminar will assume minimal background knowledge of topological groups. The thrust will be to describe key results in both topics and how our knowledge is less about the disconnected case. This talk was first given last year at the conference ”Winter of Disconnectedness“.