Syllabus

3094: Coxeter Groups
Instructor: Emily Gunawan
Office hours: see office hours, located at Monteith Bldg, room MONT 402 or the undergraduate open lounge next door Instructor’s schedule: See instructor’s regular schedule here
Class location: MONT320, see Fall 2018 math course schedule Meeting times: Tue Thurs 3:30 - 4:45
Course website: egunawan.github.io/coxeter
Course Piazza: piazza.com/uconn/fall2018/3094/home and Piazza sign up link
Main Textbooks (no purchase required):

Other group theory references:

More Coxeter groups resources:

Software: While doing some computations by hand is generally essential for learning, having software that can do bigger computations or check one’s work is very useful. The free open-source computer algebra system SageMath has an extensively-developed collection of objects and algorithms implemented for algebraic combinatorics with various documentation including thematic tutorials. More SageMath resources: + SageMath quick reference sheet for abstract algebra + Group Theory and SAGE: A Primer by Robert Beezer from 2009

course overview.

A Coxeter group is a collection of “symmetries” that have properties similar to mirror reflections. The theory of Coxeter groups is a fundamental and active area of research, with a beautiful interplay of algebraic, combinatorial, and geometric ideas. The symmetric group, i.e., permutations of n objects, is one of the most basic examples; many facts about its structure have interesting generalizations to more general Coxeter groups.

This course will provide an introduction to the theory of reflection groups and Coxeter groups from an algebraic combinatorial point of view. We will review necessary background from linear algebra and group theory and apply them to topics such as root systems, Bruhat order, reduced words, and classifications of finite reflection groups. While the course is primarily targeted at mathematics students, the subject matter would be of interest (and possible use) in the natural sciences.

After the basic material is covered, we will draw some connections to current research topics in algebraic combinatorics.

Affine G2 Dodecahedron S4 weak order Tesselation hyperbolic plane


exams and final.

There will be two in-class exams (will be announced on schedule) and a final project. Please speak to me soon if you will have a conflict or would need accomodation such as private space, extra time, etc (via Accessibility Services for Students).

take-home problem sets.

They will consist of current and past topics. I ask that you work on the rough drafts with others on these take-home problem sets, so that you can practice doing math collaboratively. Afterwards, you must do the write up on your own. If you are unsure about your solutions (and even if you are), you are encouraged to meet with me to go over your work before you submit it. All take-home problem sets will be submitted via an Overleaf link (with edit permission, so that I can make comments). Please sign up for an Overleaf account on https://www.overleaf.com.

study groups.

If you can not find a study group, e-mail me so that I can help you get involved. I assume that you will be working in groups when I make up the assignments.

Blackboard HuskyCT.

All announcements will be made on this course website. You can view your grades on HuskyCT lms.uconn.edu. If you do not have a NetID and password set up yet, please visit netid.uconn.edu to set yours up.

technology

No technology (including calculator and phone) may be used during in-class assessments.


grading.

Grades will be determined as follows:

Homework and in-class activities 40%
exams 60%


midterm grade report.

I will submit a (temporary) midterm grade report by the end of week 6 for grades lower than B-. For simplicity, I will not include +/-.

Grading questions.

Please let me know ASAP (but within one week) if I’ve made mistakes in grading your assessments. This should be done during office hours (as opposed to in class).


mental wellbeing.

Strained relationships, increased anxiety, alcohol or drug problems, feeling down, difficulty concentrating, or lack of motivation may affect a student’s academic performance or reduce a student’s ability to participate in daily activities. If you or someone you know expresses such health concerns or experiences a stressful event that can create barriers to learning, UConn services are available to assist you. Learn about confidential health services available on campus at counseling.uconn.edu Arjona Building, 4th floor, near Mirror Lake phone 860-486-4705. See also dos.uconn.edu/student-resources/.

If you see this sentence, please email me a fun picture of huskies.

accommodation services.

The Center for Students with Disabilities (CSD) wants to ensure students with disabilities have the same access to programs, opportunities and activities as all others at UConn. If you think you have short-term or long-term disability, consider going to Accessibility Services for Students accessibility.uconn.edu/students/ or contacting CSD at 860-486-2020 or csd@uconn.edu for general information or to request a (confidental) student accommodation.

student conduct code.

UConns Student Conduct Code community.uconn.edu/the-student-code includes both academic integrity and compliance with the policy against discrimination, harassment, and interpersonal violence.

academic integrity.

It is in everyone’s best interest to maintain their academic integrity. Any form of academic dishonesty undermines the goals of our course and devalues the learning process. Academic dishonesty is a serious offense at UConn and will result in an academic misconduct report and a failure in Math 3094. For more information, consult UConns guidelines for academic integrity: community.uconn.edu/the-student-code-appendix-a.

using peers and technology as resources.

Unless stated otherwise, in this particular course (only this class - you should check with your professor for each class), you are free to work with other people and use technology on take-home assigments to aid your learning. Whenever you work with another person or get help from a different book or the internet on a take-home assignment, please credit them - write the person’s name, website address at the top of your submission.

Working with other people on mathematics is highly encouraged and fun. You may work with anyone on your take-home problems. but make sure to write up your final draft by yourself.

Policy Statements.

Please refer to http://provost.uconn.edu/syllabi-references/ for the common policies we follow at UConn.