A principal theme of Geometric Group Theory is the study of non-positively curved groups. A group G is non-positively curved if it acts by transformations (in a sufficiently good manner) on a space X, whose geometry is similar to the geometry of a Euclidean or Hyperbolic space. In the presence of such an action, the properties of X give a lot of information about the structure of G and vice-versa.
One of the most natural ways to study an infinite discrete group G is to look at its finite quotients. However, for some groups this approach is completely fruitless; e.g., there exist infinite groups which have no non-trivial finite quotients at all. To measure how well can a given group be approximated by finite groups, various 'residual properties' of groups, such as residual finiteness, conjugacy separability, etc., were introduced.
Non-positively curved groups tend to be relatively nice from this viewpoint, and this project concentrates on the interaction between the geometry of the group and its residual properties.