Geometric Group Theory
Georg Lehner
Additional information / Pre-requisites
Aimed at: Bachelor and masters students
Prerequisites: Group theory. Additionally either Geometry (especially elementary non-euclidean geometry) and/or Topology (point-set topology) can be helpful.
Comments
Groups are best understood as symmetries of mathematical objects. Whereas finite groups can often be completely understood by their actions on vector spaces, this approach will often fail with infinite groups, such as free groups or hyperbolic groups. Geometric group theory tries to construct natural geometric objects (topological spaces such as manifolds or graphs for example) that these groups act on and allows one to classify the complexity these groups can have.
In this seminar, we will follow Clara Löh's book on the subject. Topics will include Cayley graphs, free groups and their subgroups, quasi-isometry classes of groups, growth types of groups, hyperbolic groups and the Banach-Tarski theorem.
Suggested reading
Clara Löh - Geometric Group Theory
12 Class schedule
Regular appointments