50 Years of Expansion in Groups

I plan to survey the many ways we have today of constructing expanding Cayley graphs of finite groups, and the ideas behind their analysis (some useful beyond that purpose). I want to highlight that despite a comprehensive understanding of achieving this for simple groups, we are far from understanding expansion in non-simple groups. I will present several concrete open questions regarding this.

No special background will be assumed: I plan to provide the group theory and representation theory background needed.