## EVENT DETAILS AND ABSTRACT

**Number Theory**
**Title:** The stable cohomology of congruence subgroups

**Speaker:** Frank Calegari

**Speaker Info:** Northwestern

**Brief Description:**

**Special Note**:

**Abstract:**

In a fixed degee d, the integral homology groups H_d(SL_N(Z),Z) are
independent of N for large N, and are intimately related to the algebraic K-theory of Z. On the other hand, if Gamma_N(P) is the congruence subgroup of Gamma_N, then H_d(Gamma_N(Z),Z) will *not* be stable, even for d = 1. We show how one can repair this (at least conjecturally), and why these groups ultimately are connected to
p-adic zeta functions.

**Date:** Monday, February 4, 2013

**Time:** 3:00PM

**Where:** Lunt 107

**Contact Person:** Simon Marshall

**Contact email:** slm@math.northwestern.edu

**Contact Phone:** 847-467-0715

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