The celebrated theorem of Gromov in 1980 asserts that any finitely
generated group with polynomial growth contains a nilpotent subgroup
of finite index. Alternative proofs have been given by Kleiner in
2007, Shalom--Tao in 2009, and Breuillard--Green--Tao 2011. In this
talk, I will give yet another proof of Gromov's theorem, along the
lines of Shalom and Chifan--Sinclair, which is based on the analysis
of reduced cohomology and Shalom's property HFD.