Course Information


Dr. Lawrence Reeves, The University of Melbourne & Dr. Anne Thomas, The University of Sydney


Groups and geometry are ubiquitous in mathematics.

This course will introduce students to the study of infinite groups from the geometrical viewpoint and will draw on ideas from low dimensional topology and from hyperbolic geometry, while making connections to analysis and algebra as well.  

The principal focus is the interaction of geometry/topology and group theory: through group actions and suitable translations of geometric concepts into a group theoretic setting.

Course Overview:

  • Free groups, presentations
  • Decision problems
  • Cayley graphs, word metrics and coarse geometry
  • Hyperbolic groups
  • Amenable groups
  • Right-angled Coxeter groups

Contact Hours:

28 hours.


Please see the Timetable for scheduled class times during the AMSI Summer School 2017.
Please note: Geometric Group Theory is held concurrently with Computational Mathematics and students cannot attend both courses in 2017.


The required background is a first course in group theory.


  • Assignment 1: 15%
  • Assignment 2: 15%
  • Assignment 3: 20% (including a special project worth 5%)
  • Final Examination: 50%


Lecture notes (to be provided), plus additional references (available soon).

Lecturer Biographies

Geometric Group Theory

Dr. Lawrence Reeves, The University of Melbourne

Lawrence is a Lecturer at the University of Melbourne. He is interested in all aspects of geometric group theory, in particular notions of curvature and boundaries at infinity. After completing his PhD at the University of Melbourne he held positions at Hebrew University of Jerusalem, Oxford University and the University of Aix-Marseille.

Geometric Group Theory

Dr. Anne Thomas, The University of Sydney

Anne works on geometric group theory and is interested in finding connections between this field and other areas of mathematics. She is a Senior Lecturer at the University of Sydney and recently spent a semester teaching an advanced course on Coxeter Groups and Buildings at ETH Zurich.

Anne was an undergraduate at UNSW, received her PhD from the University of Chicago in 2007 and has also held positions at the Mathematical Sciences Research Institute, Cornell, Oxford and Glasgow.

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