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.