This course will introduce the audience to different aspects of geometry group theory. The starting point is the introduction of the Calyley graph of a finitely generated group and geometric notion of quasi-isometry. Subsequently, four different topics are discussed:
    • Growth in groups and Gromov’s theorem on virtually nilpotent groups
    • Hyperbolic groups and the Gromov boundary
    • Ends and Stalling’s theorem
    • Amenability

The subject of geometric group theory displays lively interaction with many other areas of mathematics, such as algebraic topology, combinatorial group theory, Lie groups and operator algebras.

Literature: The main resource for the course will be Löh’s book “Geometric Group Theory – An Introduction”. The following additional references can be usefull
    • Bridson Haeflinger - “Metric spaces of non-positive curvature”
    • De la Harpe - "Topics in Geometric Group Theory"
    • Druţu Kapovich - “Geometric Group Theory”

Prerequisites: The course assumes only basic knowledge in
    • Group theory,
    • Graph theory, and
    • Metric spaces.