MAT 382H1F, Introduction to Geometric Group Theory, Fall 2020

Instructor

Prof. Kasra Rafi

Office: BA 6236 (Bahen Centre)
Email: rafi@math.toronto.edu

Meetings

Mondays 1-2 pm on zoom.
Friday 2 - 4 pm in zoom.

Please check the minimum technical requirement
For student Tech Support see here

If you are interested in auditing the course,
e-mail me to receive a zoom link.

Office hours

Mondays and Wednesdays 5-6 pm
(or by appointment) on zoom.

Teaching Assistant

Ali Pirhosseinloo

E-mail: ali.pirhosseinloo@mail.utoronto.ca

Ali will hold weekly virtual office hours on Thursdays 4-5 pm. You can stop by to get help with the homework or to discuss the grading of the homework or the midterm.

Textbook

Office Hours with a Geometric Group Theorist, by Dan Margalit and Matt Clay (Main)
Trees, by Jean-Pierre Serre (supplementary)).
An Introduction to Geometric Topology, by Bruno Martelli (supplementary). Metric spaces of non-positive curvature, by M. Bridson and A. Hafliger (suplimentary).

Course description

Felix Klein famously said "Given a manifold with its associated transformation group, one should investigate those structures of the manifold that have properties which are invariant under the transformation group." Conversely, it turns out that the algebraic properties of a group are often reflected in the geometry of spaces they act on. We will try to understand groups by examining their inherent geometry.

Marking scheme

Your course grade is computed as follows:

• Homework 20%
• Class Project 25%
• Midterm 20%
• Final assessment 35%

Homework and Class Project:

There will be 4 homework assignments and a longer assignment called the Class Project. The class project can be chosen from the projects given in the textbook (after discussing with me) or any topic related to in class dicussions. The Class Project has a written and presentation component. Students are encouraged to work together on the homework problems but have to write their own solutions.

• Problem Set I, Due September 28, Chapters 1, 2 and 3.
• Problem Set II, Due October 19, Chapters 4 and 5.
• Problem Set III, Due November 16, Chapters 7 and 9.
• Problem Set IV, Due December 7, Chapters 13, 15 and 16.

Here are the Class Projects that were pesented in class.

• Anthony Wallace
• Elnaz Hessami
• Fedor Prikolab
• Kunal Chawla
• Vivian He

Midterm and the Final Assessment

There will be an in class Midterm on October 23, that is, the exam will take place during the class time but online. The Final exam will also take place online. The final exam will be an oral exam.

Study hints

You should read the relevant parts of the textbook, ideally before the lectures in class on the same material, and attempt most of the exercises in the textbook. Make sure to ask questions during class. Questions slow the pace and give everyone time to think about what is being said. Use the office hours, talk to each other and talk to the TA. The more time you spend with the material the more intuitive the concepts of the course will become. Try to find a topic for your Class Project early.

Policy on missed exams:

Verification of Illness (also known as a "doctor's not") is temporarily not required. See here

Prerequisite

MAT224H1/MAT247H1, MAT347, MAT327..

You need to be comfortable with proofs and with using the language of writing mathematics.

Academic integrity

The University of Toronto Code of Behaviour on Academic Matters can be found here.

Accessibility needs

The University of Toronto is committed to accessibility. If you require accommodations for a disability, or have any accessibility concerns about the course, the classroom or course materials, please contact Accessibility Services as soon as possible: email accessibility.services@utoronto.ca or visit here.

Mental Health Care

The Health and Wellness Centre offers mental health services to students. To get more information, visit their website here.