Eisenstein cohomology and automorphic $L$-functions

During the past ten years of the most inspiring and very fruitful collaboration with Joachim Schwermer,
we have carefully studied the non-vanishing conditions for certain summands in the decomposition
along the cuspidal support of the (square-integrable) Eisenstein cohomology of a reductive group over
a number field. These conditions form a subtle combination of geometric conditions, arising from
cohomological considerations, and arithmetic conditions, arising from the analytic properties of
Eisenstein series and given in terms of automorphic $L$-functions. In the talk I will give a survey
of the most important results of our long-lasting collaboration.