Geometric Group Theory

Groups are abstract algebraic constructions closely related to the idea of symmetry. Geometric group theory is the subject of active research in mathematics that uses tools from graph theory, geometry, and topology to study infinite groups. We will begin with a review of group theory and an introduction to the geometric tools we will need. Collectively, we will use these tools to study free groups and hyperbolic groups, among others. Students will then independently investigate a particular type of group or group property. Students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. Fulfills the capstone senior work requirement for the mathematics major. (Approval required and MATH 302) 3hrs sem.