Gromov’s polynomial growth theorem revisited
We explain how to deduce Gromov’s polynomial growth theorem from the Breuillard-Green-Tao theorem on the structure of finite approximate groups. The proof is similar to Hrushovski’s proof, but due to the more quantitative results of BGT it is more robust. We use this additional robustness to prove a version of Gromov’s polynomial growth theorem for approximate groups. This talk is based on joint work with Cordes, Machado and Tonic.