Talk 1: Hidden objects - On arithmetically defined hyperbolic 5-manifolds and their cohomology

The talk begins with an expository discussion of the cohomology of non-uniform arithmetic groups, emphasising the problem of constructing cohomology classes of specific types.
Then we consider the significant example of arithmetically defined quotients of (products of) hyperbolic 5-space. Using geometric and automorphic methods we sketch various constructions of classes in these cases.