# On Eisenstein Series and the Cohomology of Arithmetic Groups

 JOINT IAS/PU NUMBER THEORY SEMINAR Topic: On Eisenstein Series and the Cohomology of Arithmetic Groups Speaker: Joachim Schwermer Affiliation: University of Vienna, ESI Date: Thursday, February 25 Time/Room: 4:30pm - 5:30pm/S-101

The automorphic cohomology of a reductive $\mathbb{Q}$-group $G$, defined in terms of the automorphic spectrum of $G$, captures essential analytic aspects of the arithmetic subgroups of $G$ and their cohomology. We discuss the actual construction of cohomology classes represented by residues or principal values of derivatives of Eisenstein series. We show that non-trivial Eisenstein cohomology classes can only arise if the point of evaluation features a 'half-integral' property. This rises questions concerning the analytic behavior of certain automorphic L-functions at half-integral arguments.