Math.Koll. am 31. Mai 2006/ Prof. Zalesskii

[Institut für Mathematik]

Mathematisches Kolloquium

EINLADUNG

zu einem

VORTRAG

von

Prof. Pavel Zalesskii (University of Brasilia)

mit dem Thema:

''The congruence subgroup problem:
profinite aspect''

Abstract: We begin with a detailed formulation of the congruence subgroup
problem for the group $SL_2(\mathbb{Z})$ and its negative solution
discovered by Fricke and Klein. We shall then discuss how the congruence
subgroup problem generalizes to arbitrary linear groups over arithmetic
rings. After that we shall review the first positive results in the
congruence subgroup problem obtained by Bass-Lazard-Serre, Mennicke and
Bass-Milnor-Serre in the late 60s. The centerpiece of this lecture will be a
detailed discussion of the notion of {\it congruence kernel} introduced by
Serre. We will explain why nowadays by the congruence subgroup problem
people mean the problem of computation of the congruence kernel. We shall
discuss then the congruence kernel for $SL_2$ and present new results on its
description  for some arithmetic lattices of  algebraic groups of rank 1.

Zeit: Mittwoch, 31. Mai 2006,
        15.00 Uhr (Kaffeejause), anschlieszend 15.15 Uhr Vortrag

Ort: Fakultaet fuer Mathematik der Universitaet Wien, Nordbergstr. 15,
       Seminarraum C 2.09

Harald Rindler
Karl Auinger