Joint IAS/PU Arithmetic Geometry

The compactly supported cohomology groups of the locally symmetric space for $GL_n(Z)$ form, as n varies the $E_1$ page of a spectral sequence. This spectral sequence was introduced by Quillen in 1973 in his proof of finite generation of $K$-groups, but also seems independently interesting as an organizing tool. I will discuss joint work with Brown, Chan, and Payne on algebraic structures in this spectral sequence and a relationship to certain "graph complexes" introduced by Kontsevich in the 1990s.