Title: What are amenable groups and why are groups non-amenable
Abstract: I will give an introduction to amenable
groups and explain the result of Kevin Whyte that a
countable non-amenable group admits a
"translation-like" action by a non-abelian free group.
I will also discuss (without proof) a measure theoretic
analogue of this result due to D. Gaboriau and R. Lyons.