Everytopic Seminar

 March 14th, 2008, 1:40 pm – 3:00pm, Goldsmith 226

 

 

Title: Stable Group Homology and Hecke Operators

Speaker: Avner Ash, Boston College

 

Abstract:

About 30 years ago Ruth Charney proved that the homology of the

general linear group stabilized.  In the case of GL(n,Z) this means that

if M is any constant coefficient module and r is fixed, H_r(GL(n,Z),M)

doesn't depend on n if n is sufficiently large.  Recently, Frank Calegari

and Akshay Venkatesh asked: how do the Hecke operators act on the stable

homology?

 

In the first half of my talk I will review group homology, Hecke

operators, and the connection with Galois representations.  In the second

half I will investigate how the Hecke operators act on the stable homology

and show that the Hecke eigenvalues correspond to Galois representations

which are isomorphic to direct sums of powers of the cyclotomic character.