Special Topics in Algebra Summer Term 2019

On Wednesday, July 3, the class will be in SR 2. The class starts as usually at 4pm (st).

 

Dates: Wednesday at 4 pm (st) in HS IV.


Lecturer: Prof. Dr. Gabriela Weitze-Schmithüsen

contact: weitze [at] math.uni-sb.de
office hours: please contact me by email or just check whether I am here (room 301, E 2.4)

 

Topics:

In this lecture we will study subgroups of the matrix group SL(n,Z) of matrices with determinant 1. There are two different classes of subgroups, namely arithmetic groups and thin groups. The study of these groups is related to several interesting problems in number theory and geometry. Recently,  it  has  become  a  ”hot  topic”  in  the  context  of  the super strongly approximation theorem, which states a condition that certain families of finite graphs related to these groups are expander graphs. Up to now it is a hard problem to decide whether a given group is arithmetic or thin.

 

Prerequisites:

 Algebra

 

Literature:

  •  What Is ... a thin Group? (for a first glance on the topic)
  •  Luis Ribes, Pavel Zalesskii: Profinte groups (Springer 2000, 2010)
  •  AlexanderLubotzky, Dan Segal: Subgroup Growth (Birkhäuser 2003)