Geometric Group Theory

Course Number: 
Hours - Lecture: 
Hours - Lab: 
Hours - Recitation: 
Hours - Total Credit: 
Typical Scheduling: 
Not regularly scheduled

Special topics course on Geometric Group Theory, offered in Spring 2021 by Dan Margalit.


MATH 4107 and MATH 2106  or permission of instructor

Course Text: 

Text: Groups, Graphs, and Trees, John Meier

Supplementary text: Office Hours with a Geometric Group Theorist, Matt Clay and Dan Margalit

Topic Outline: 

Geometric group theory is the study of group actions on geometric spaces.  A basic theorem in the subject is: if a group acts freely on a tree then the group is free.  Geometric group theory is an exciting and active area of research that is very accessible to undergraduates.

The course will roughly follow Meier's textbook: background on group theory and group actions, Cayley graphs, groups generated by reflections, groups acting on trees, Baumslag-Solitar groups, the word problem, lamplighter groups, Thompson groups, hyperbolic groups.

In our algebra sequence, the students don't see a lot of interesting infinite groups.  Geometric group theory is a study of this wide, beautiful, and wonderful world.