Noa Vikman: Recent Proofs of Gromov's Theorem on Groups of Polynomial Growth

Gromov’s theorem on finitely generated groups of polynomial growth is one of the cornerstones of geometric group theory. It has seen many applications and has immense importance within its realm. However, the early proofs of Gromov’s theorem were based on deep results and were practically unsuitable for teaching. Recently, a new family of proofs have been published, potentially providing new ways to learn and teach Gromov’s theorem. Specifically, in a blog post from 2010, Terence Tao outlines an elementary proof, inspired by a proof of Bruce Kleiner.

In this talk we will explore a brief theoretical background to Gromov's theorem and its different proofs, and then we will discuss the elementary proof of Tao, which was the main focus in the speaker's degree project of the same title as this talk. In particular, the main contribution of the speaker in his degree project is providing a significant amount of additional detail, and providing theoretical clarifications to all the steps in the proof. These contributions can be helpful to learners, and they also enforce the legitimacy of Tao's proof.