MAT 444-01 - Senior Seminar: Geometric Group Theory

4 credits (Spring)

Despite its role as a cornerstone of abstract algebra, group theory is an intrinsically geometric subject. From the work of Klein in the late 19th century to Gromov’s foundational results nearly a century later, geometry has proven to be a powerful tool and a natural way to understand groups. The connections between these two areas, together with subjects such as topology, combinatorics, and formal language theory, form the basis for the field known as geometric group theory.

In this course we will take an in-depth tour of several topics in geometric group theory, focusing especially on the interactions between groups and graphs. As part of the course, students will have the opportunity to complete a research project which explores a chosen topic in detail, including its relevance to geometric group theory and neighboring fields.

Prerequisite: MAT 321 . Recommended - MAT 316 . Exposure to combinatorics will be useful, but not required.
Instructor: Dougherty