John Mackay University of Oxford The boundary at infinity of a hyperbolic group has a natural invariant called its conformal dimension. This analytic invariant of the boundary can be studied using l_p-cohomology of the group. I will discuss how recent work of Bourdon, Kleiner and others combines with ideas of Ollivier and Wise to give new insights to the geometry of small cancellation groups; in particular, to certain random groups.