Syllabus for Math 8851.
Syllabus for Math 8851 (Combinatorial and Geometric Group Theory) Spring 2023
MW 5-6:15 pm, Kerchof 317.
- Instructor: Mikhail Ershov
- Office: Kerchof 302
- e-mail: ershov at virginia dot edu
- Office hours: TBA
- Course webpage: https://m-ershov.github.io/8851_Spring2023/
Course outline
The current plan is to cover the following topics:
1. Free groups and presentations of groups by generators and
relations (6 lectures)
2. Free products with amalgamation, HNN-extensions and an overview of the Bass-Serre theory (3 lectures)
3. Word growth in groups (5 lectures)
4. Burnside problem(s) (5 lectures)
5. Amenable groups and sofic groups (5 lectures)
6. Hyperbolic groups (4 lectures)
References
There is no official text for the course. Most (but not all) of the
material we will discuss is covered by the following books:
- Combinatorial group theory by W. Magnus, A. Karrass and
D. Solitar
- Combinatorial group theory by R. C. Lyndon and
P.E. Schupp
- Geometric group theory by C. Drutu and I. Kapovich,
draft available here
- Topics in Groups and Geometry. Growth, Amenability, and Random Walks by
T. Ceccherini-Silberstein and M. D'Adderio ,
available via UVA subscription here
- Introduction to group theory by O. Bogopolski
- Topics in geometric group theory by P. de la Harpe
- A course in the theory of groups by D. Robinson
Prerequisities
The course should be accessible to students who have
completed first year graduate courses. The main
prerequisite is a good knowledge of basic group theory at the
level of
Math 7751. However, occasionally we will use results from other areas, including topology (mainly
covering spaces), linear algebra and ring theory.
Homework and Problem Session
- Homework will be assigned regularly (most likely weekly)
- Approximately every two weeks we will have a problem session
(date and time TBD) where homework problems will be discussed.
- Students taking the class for a grade are expected to
- seriously attempt all the assigned problems
- present homework problems during the problem sessions on the regular basis
End of the semester Presentations
Each student taking the class for a grade must give a 40 minute presentation on a chosen topic at the end of the semester.
A list of suggested topics will be
provided. You should feel free to choose a different topic (not
from the list), but you need to get my approval. In any case, you should inform me
about your proposed topic no later than the end of March.
Add/drop/withdrawal dates:
- Wednesday, February 1 -- Last day to add a course, select the AU (audit) option or change to or from "Credit/No Credit" Option
- Thursday, February 2 -- Last day to drop a course
- Wednesday, March 15 -- Last day to withdraw from a course
SDAC
All students with special needs requiring accommodations should present the appropriate paperwork from
the Student Disability Access Center (SDAC). It is the student's responsibility to present this paperwork in a
timely fashion and follow up with the instructor about the accommodations being offered. Accommodations
for test-taking (e.g., extended time) should be arranged at least 5 business days before an exam.