Automorphic cohomology, motivic cohomology, and the adjoint $L$-function
  We propose a relationship between the cohomology of arithmetic groups, and the motivic cohomology of certain (Langlands-)attached motives. The motivic cohomology group in question is that related, by Beilinson's conjecture, to the adjoint $L$-function at $s=1$. We present evidence for the conjecture using the theory of periods of automorphic forms, and using analytic torsion. 
Kartik Prasanna and Akshay Venkatesh
math.NT