# Research Group: Geometric Group Theory

The central idea of Geometric Group Theory is to study discrete groups by viewing them as metric spaces, using for example a word metric. Gromov introduced this viewpoint, with his idea of hyperbolic groups and with his proof of a conjecture of Milnor. A key idea in Gromov's proof was that when `viewed from far away', a free abelian group starts to look like a real vector space.