Kleiner's proof of Gromov's theorem

Terence Tao
University of California, Los Angeles (UCLA)

Recently, Bruce Kleiner gave a new proof of Gromov's celebrated theorem that all groups of polynomial growth are virtually nilpotent, by using an elementary Poincare inequality on the Cayley graph to bound the dimension of harmonic functions on the group. In this talk we sketch the main ideas of Kleiner's proof.

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