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.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/11596