Geometric Group Theory (GGT) is a relatively new mathematical discipline which has had significant impact on the much older disciplines of geometry, topology, and algebra. In recent years, major open problems have been solved using GGT methods. Plus, it's a beautiful subject! There are pretty pictures, elegant examples, clever theorems, and significant new ways of looking at classical objects (such as graphs and groups.) Roughly speaking, GGT uses geometric and topological methods to study (usually infinite) groups and uses algebraic methods to study geometric and topological spaces. This merger of different mathematical disciplines makes GGT a perfect topic for a major capstone course.
- Comments on how symmetries give rise to permutations of subsets.
- Group project 5 on constructing fundamental domains. The other group projects are linked from the homework page.
- Notes on Free Groups
- Exam 1 Study Guide
- Final Project Assignment Guide
