Math 503, Spring 2024

MATH 503, Spring 2024. Introduction to geometric group theory.

Course announcement.
Professor: Igor Mineyev.
Class time and place: MWF 3:00-3:50p.m., 104 English Building.
Office hours: for now are scheduled on Zoom for Monday and Wednesday at 6:00pm on Zoom to make it after the classes, if this is fine with the students. (The office hour for my other class is at 5.p.m., which you might also use if no one comes from that class.) The meeting number and password is given in class. Please come at the beginning of the hour, because we might leave earlier if there are no questions.
Use this as "Ask me anything session". We can discuss any mathematical topic you find interesting.
In those rare situations when you need to talk to me privately, let me know during our Zoom meeting or before, then call me after the meeting is finished.

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. Face-to-face communication (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.

There is no standard textbook for the course. If you are interested in learning geometric/combinatorial group theory in depth, I very much encourage you to click on THINGS RELATED TO GEOMETRIC GROUP THEORY. (Hint: pretty much anything is related.) Take a look at the list of references there, feel free to discuss any topics with me.

Homework will appear here. Please hand it in handwritten and stapled at the beginning of the class. Here are links to the study explaining how handwriting is good for you: handwriting1, handwriting2. Write the class number and the homework number. By hand.

The grade will be based on attendance and homework. Actively participating in class is a very good idea too. One lowest homework assignment will be dropped. Grading will use the standard scale: A-,A,A+ are 90 to 100; B-,B,B+ are 80 to 90; C-,C,C+ are 70 to 80; D-, D,D+ are 60 to 70. The grades will be posted on Learn@illinois Moodle: look for "MATH 503 G1 SP24: Intro Geometric Group Theory (Mineyev, I)".

The online evaluation forms for this class should be available some time, probably between April 19 and May 1, 2024. You either receive this information by email or directly log in on the website https://go.illinois.edu/ices-online. I very much encourage you to fill out the evaluation forms. Since there is a deadline, please try not to miss it.

Various other links related to geometric group theory:

As part of the ongoing IG³OR'S group, please feel free to join our weekly mini-seminar on Zoom in Spring 2024 (the meeting number and password were given in class). Xianhao An, Jihong Cai and Leslie Hu will read and present several articles by Akio Kawauchi that claim to have solved several long-standing open problems in topology/geometric group theory. Feel free to read the articles as well and try to find mistakes, if any. We meet on Tuesdays at 9.30 am.
IML (Illinois Mathematics Lab, formerly known as Illinois Geometry Lab) here at UIUC . The earlier you start doing research in math, the longer you will do it. :)
ColorTaiko!: the IML project that I am running starting in Spring 2024. The fun game that we will create in that project is secretly related to several long-standing open problems about group algebras called Kaplansky conjectures. My article showing the connection between the Kaplansky conjectures and the ColorTaiko! game will appear at some point on my website.
U of I Math seminars.
All kinds of pictures of topological spaces at Sketches of topology.
A list of resources about geometric group theory by Jon McCammond.
Open problems in low-dimensional topology.
Open problems listed by AIM, including some from geometric group theory.
Questions in geometric group theory by Mladen Bestvina.
Problems on boundaries of groups and kleinian groups by Misha Kapovich.
Unsolved problems in algebra.
Unsolved problems in group theory.
Open problems in combinatorial and geometric group theory by Baumslag-Myasnikov-Shpilrain. Here is an archived online version of this list. It does not seem to be updated, but still is a good source.

Back to Igor Mineyev's math page.