The conformal dimension of a hyperbolic group is a powerful numeric quasi-isometry invariant associated to its boundary.
As an invariant it is finer than the topological dimension and allows us to distinguish between groups with homeomorphic boundaries.
I will start by talking about what conformal geometry even is, before discussing how this connects to studying the boundaries of hyperbolic groups.
I will probably end by saying how jolly hard it is to compute.
- Junior Topology and Group Theory Seminar