Gromov's theorem on groups of polynomial growth

Abstract: 

A finitely generated group has polynomial growth if the set of all elements which may be expressed as a product of at most $n$ generators and their inverses grows polynomially in $n$.  Gromov proved that every finitely generated group of polynomial growth is a finite extension of a nilpotent group.  This theorem has been reproved and simplified by various people, including Kleiner, Shalom and Tao.  The aim of the seminar is to explain the significance and proof of the theorem.