While many properties such as amenability, property (T) and FA, finiteness properties, Euler characteristic, ... can differ for profinitely isomorphic groups, we present a result in the positive direction: The covolume of lattices in higher rank Lie groups with the congruence subgroup property is determined by the profinite completion. Without relying on CSP, we additionally show that volume is a profinite invariant of octonionic hyperbolic congruence manifolds. Joint work with Steffen Kionke and Ralf Köhl.
