MATH 503, Spring 2020.
Introduction to geometric group theory.
Professor: Igor Mineyev, 243 Illini Hall.
mineyev illinois edu
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.
Class time and place: MWF 3:00-3:50p.m., 443 Altgeld Hall.
Office hours. Monday and Wednesday, 4:10-5:00p.m., Illini Hall 243.
Because of COVID19, this course
and many other courses will transition to an online format, at least for the two weeks
after the spring break. I am learning what can and will be done. Prepare for a wild ride. We will need
to implement a least-disruptive plan possible. As we proceed, more information will be posted here. Please check this page in the coming days and weeks.
- For now, try not to travel, try to stay in your home location.
- I believe, the interactivity of classroom setting is important, this is why
it is important to meet in class regularly. The current situation with COVID19, of course,
prevents us from doing that for the rest of the semester. My preference will be to have a synchronous meetings at the regular class time by Zoom. Giving a lecture at that
time does not seem to be feasible. Instead, we will discuss things at class time.
- We will do some independent reading.
Sometimes I might record lectures and post videos for you to see.
RIGHT NOW, if you have not done this before, please login at least once
(link on upper right) using your university NetID and password.
This way I will be able to add you to the channel
titled "2020s Math 503 by Igor Mineyev", where you can view videos for this class.
If you can access the videos now, please watch the lectures any time before we meet.
And you should be able to post videos to this channel as well, if needed.
- Start preparing in advance. Install the Zoom app on your device well in advance of the first class:
Make an account with Zoom. Please use your University email address
(ending with @illinois.edu) when creating that account. Type your full name in Profile,
to be displayed during the virtual meetings. Get accustomed with the program. Be prepared to join our first virtual meeting on Monday, March 23, 2020, at 3 pm central time. Join Zoom meeting
meeting ID is 205 921 9133.
It seems that https://illinois.zoom.us/
is the right address to use when joining a meeting, but I am not sure.
- High-speed internet access is strongly recommended. 1.5 Mbps or more is recommended for Zoom. To minimize noise during the meeting, mute your microphone
(this is an option within Zoom, on the lower left).
- For the meetings, be in a non-distracting environment.
I thought it is better to keep your web camera on during the lecture, but it looks like turning it off
is better for bandwidth reasons. Let's try it both ways at our first meeting to see how it works.
If you want to ask a question, there are 2 options: (1) raise your hand virtually or literally
(if I can see you), or (2) unmute the microphone, ask, then mute it again.
- I will be using Learn@Illinois Moodle for homework assignments.
Please scan your homework into a file, or type it in latex.
PDF files are strongly preferred for uploads, whenever possible.
If you scan it or take a picture, please write legibly and scan with
a sufficiently high resolution. To upload your file, log in using your NetID at
For help with Learn@Illinois Moodle see these links:
For the future homework assignments the deadline will probably be at 6pm on Friday
it is due. Do not wait until the deadline,
submit your homework as early as possible.
- For office hours, my plan for now is to use the regular
class time for all discussions, in effect making it an office hour. The regular class time is preferred, but
if it is hard for you to make it at that time (if you are in a very different time zone), please talk to me at least once, so that we can make some arrangement.
The grade will be based on attendance and homework. Actively participating in class is a very good idea too.
There is no standard textbook for the course.
If you are interested in learning geometric/combinatorial group theory in depth,
here is an incomplete list of books related to the subject, in no particular order.
- Magnus, Karras, Solitar. Combinatorial group theory.
- Lyndon, Schupp. Combinatorial group theory.
- Bridson, Haefliger. Metric spaces of non-positive curvature.
- Ghys, Haefliger, Verjovsky. Group theory from a geometrical viewpoint.
- Ken'ichi Ohshika. Discrete grops.
- John Meier. Groups, graphs and trees: an introduction to the geometry of infinite groups.
- Colins, Grigorchuk, Kurchanov, Zieschang. Combinatorial group theory and applications to geometry.
- Gersten (editor). Essays in group theory. MSRI publications.
- Ghys, de la Harpe. Sur les groupes hyperboliques d'apres Mikhael Gromov.
- Bedford, Keane, Series (editors). Ergodic theory, symbolic dynamics and hyperbolic spaces.
- Ross Geoghegan. Topological methods in group theory.
- Michael Davis. The geometry and topology of Coxeter groups.
- Pierre de la Harpe. Topics in geometric group theory.
- Epstein (editor), Cannon, Holt, Levy, Paterson, Thurston. Word processing in groups.
- Hog-Angeloni, Metzler, Sieradski (editors). Two-dimensional homotopy and combinatorial group theory.
London Mathematical Society Lecture Note Series, 197.
- Coornaert, Delzant, Papadopoulos. Géométrie et théorie des groupes.
- John Hempel. 3-manifolds.
- Kenneth Brown. Cohomology of groups.
- Scott, Wall. Topological methods in group theory.
Ilya Kapovich, Nadia Benakli. Boundaries of hyperbolic groups.
Cornelia Drutu, Michael Kapovich. Geometric group theory.
Here are some interesting links related to this course.