Random Groups

Finitely presented groups are a natural algebraic generalisation of the collection of finite groups. Unlike the finite case there is almost no hope of any kind of classification.

The goal of random groups is therefore to understand the properties of the "typical" finitely presented group. I will present a couple of models for random groups and survey some of the main theorems and open questions in the area, demonstrating surprising correlations between these probabilistic models, geometry and analysis.