The Geometry of Discrete Groups

This is an introduction to the geometric approach to the theory of infinite discrete groups. Topics will include group actions, the construction of Cayley graphs, connections to formal language theory, actions on trees, volume growth, and large-scale geometry. Theorems will be balanced by specific examples such as Baumslag-Solitar groups, the Lamplighter group, and Thompson’s groups.

More complete information about the class will be available via Canvas once the semester starts.

Homework

More than half your grade will be based on problem sets. These will be due approximately weekly. LaTeX is recommended, though clearly handwritten homework will also be accepted, and drawing figures by hand is fine. Unless otherwise stated, you can discuss problems with each other but should write them up separately. Be sure to note any help you got. Looking up solutions on the internet is not allowed.

Project

Most of the rest of your grade will be based on a final project: You will write an expository paper on some aspect of geometric group theory not covered in the lectures. This work will also be presented to the class. Geometric group theory has connections to almost every area of modern mathematics. In lectures and homework we will restrict ourselves to topics which can be understood with a minimum of background, but this is an opportunity to find out t more about some connections with some other mathematics which you are interested in. The written paper will be due before the Thanksgiving break. The lectures after break will be set aside for student presentations.

References

(The links should work on campus, or off-campus, using PassKey) [M] is the main text. [CM] and [L] are supplemental, and likely to be useful sources for project ideas.
Jason Manning's home page.

Last Updated 2020-08-27