MATH 503, Spring 2026.
Introduction to geometric group theory.
Math 500 is NOT required as a prerequisite for this course.
Familiarity with standard concepts in group theory will be helpful:
group, subgroup, a generating set, group homomorphism, isomorphism theorems, etc.
If you know some standard concepts from algebraic topology (like fundamental group
and covering spaces), that might also be helpful, but not required.
Instead, feel free to take a look at my
highly unconventional introduction to both areas in Math 490 Constructive geometry:
from grounds to groups. That introduction is not required for this 503 course either,
but it might be a good discussion-starter for this course. Feel free to ask me
anything about grounds, or any math, for that matter.
Professor: Igor Mineyev.
It is better to talk to me before/during/after the class and to come to office hours
rather than to send email. Discussions are more efficient that way. I also have
a slight disability in terms of typing/email. Communication in person (virtual or otherwise) is very much preferred and appreciated.
Class time and place: MWF 3:00–3:50 p.m., 336 Davenport Hall.
Office hours: 6pm-7pm on Zoom. The password was given in class.
Grades: The grade will be based on attendance, homework (70%), and a project (30%) in the second half of the course. It is not counted if you have to miss the class once or twice for substantial reasons. If you miss
more classes, please provide a proof of substantial reason for all missed classes, otherwise this can negatively affect your overall grade for the class.
The best way to contact.
My email is mineyev at illinois edu, but I have a slight disability that makes it hard for me to type, and generally to deal with email. Vocal real-time communication is much more preferred and very much appreciated. Please talk to me before/during/after the class and during the office hours.
Communication in person (virtual or otherwise) is also much more efficient for discussing things.
I would appreciate if you use it as much as possible rather than communicate by email.
I am happy to discuss any kind of math, or any other things that you are interested in. Math is the only possible meaning of life. And fun too. Take initiative, talk to me about it. Any suggestions are also welcome.
Participation. Participation in class will not affect your grade, but is very much encouraged.
Take a look at the list of references below
and feel free to discuss any topics with me.
Homework will appear here later.
Feel free to play the visual
PathForms
game, or the
ColorTaiko!
game. Both are related to this Math 503 class.
Click on the game's title to see more information. They keep being updated
from time to time.
Various links.