Seminar on the Cohomology of Arithmetic Groups

This fall, I am organizing a seminar on the cohomology of arithmetic groups. Topics may include: the Eichler-Shimura isomorphism, Matsushima's formula, Eisenstein classes, Coherent cohomology, and possibly others.

Time and place: Tuesdays 4:30-6:00 in Mathematics 507.


[BW] Borel, A. and Wallach, N. Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups. Second Edition. AMS, 2000.
[Fra] Franke, J. Harmonic Analysis in Weighted L_2 Spaces. Annales Scientifiques de l'E.N.S., 1998.
[Jac] Jacinto, J. Cohomology of Arithmetic Groups. Notes on Matsushima's formula from Ashwin Iyengar's website.
[LS] Li, J.-S. and Schwermer, J. On the Eisenstein Cohomology of Arithmetic Groups. Duke, 2004.
[VZ] Vogan, D. and Zuckerman, G. Unitary Representations with Non-zero Cohomology. Compositio Mathematica, 1984.
[Wil] Williams, C. Automorphic Forms in Cohomology via Examples. Notes from Ashwin Iyengar's website.
[Yo] Yoshida, T. Notes on Matsushima's Formula.

Tentative Schedule:

Date Title Speaker References
September 17 Overview Sam Mundy
September 24 Eichler-Shimura Isomorphism Ashwin Iyengar [Wil]
October 1 Basic Stuff Cailan Li [BW]
October 8 More Basic Stuff Yu-Sheng Lee [BW]
October 15 Matsushima's Formula Stan Atanasov [Yo], [Jac]
October 22 Computing the Terms in Matsushima's Formula [Jac], [VZ]
October 29
November 5 No Talk: Election Day
November 12
November 19
November 26
December 3
December 10
December 17