• FU-Students should register via Campus Management.
• Non-FU-students should register via MyCampus/Whiteboard.

Summer Term 2025

Dozenten: Dr. Georg Lehner

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• Time and place:  Mondays,  2pm -- 4pm, SR 140, Arnimallee 7 (HH).

• Leistungsnachweis/criteria for proof of performance:
  Grade and credit points will be awarded based on a presentation and written summary.

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Prerequisites: Group theory. Additionally either Geometry (especially elementary non-euclidean geometry) and/or Topology (point-set topology) can be helpful.
Aimed at: Bachelor and masters students

Content: 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.

Talks

Literature:

• Clara Löh - Geometric Group Theory