# Seminar: "Calculating the cohomology of Bianchi groups" (E. Berkove, Lafayette College)

Date: Friday November 28th, 15-16.

Place: CRM, room C1/028

Title: "Calculating the cohomology of Bianchi groups".

Speaker: Ethan Berkove (Lafayette College, USA)

Abstract: Let $\mathcal{O}$ be an imaginary quadratic extension of

the rational numbers. The Bianchi groups are the matrix groups

$PSL_2(\mathcal{O})$ (or sometimes the corresponding $SL_2$ groups).

In this way, the Bianchi groups can be thought of as

generalizations of the modular group $PSL_2(\mathbb{Z})$. Bianchi

groups have been studied for over a century, in fields as varied as

group theory, number theory, and topology.

In this talk we will provide an introduction to Bianchi groups and

overview of techniques for calculating their (co)homology. Many

earlier calculations where done primarily on a case-by-case basis.

Recently, however, Alexander Rahm introduced a cellular space, the

$p$-\textit{torsion subcomplex}, on which the Bianchi groups act.

We will define this complex and describe some recent results of

Alexander Rahm and the speaker which use it.