Endoscopy and the cohomology of arithmetic groups

Given an integer k, taken to be at least 2, it is well-known that
there are holomorphic cusp forms of weight k for some subgroup of SL(2,Z).
In this talk, I will discuss some higher-dimensional analogues, which beg
the question: given a connected reductive group G, and a
finite-dimensional representation
V of G, is the cuspidal cohomology of G with coefficients in V nonzero? After
introducing the context, and discussing some general themes, I will present
some results, obtained in an ongoing collaboration with Chandrasheel
Bhagwat, that give an endoscopic construction of nonzero
cuspidal cohomology classes when G is GL(n) over a totally real field.