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):

Introduction to Group Theory, a few section from Tom Judson’s Abstract Algebra: Theory and Applications (HTML and Sage exercises)
Introduction to Coxeter groups, a few sections from Combinatorics of Coxeter Groups (Springer, 2005) by Anders Björner and Francesco Brenti.

Other group theory references:

More Coxeter groups resources:

Textbook James E. Humphreys: Reflection Groups and Coxeter Groups.
Schilling’s Coxeter groups and Schubert calculus Winter 2009 lecture notes
Online Lecture notes from CRM Winter School on Coxeter groups 2002

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%

Grade cutoffs are at most 90%, 80%, 70%, and 60% for A-, B-, C-, and D-.
Your grade does not depend on other students’ grades.

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.

For tips to minimize academic misconduct, see Protecting yourself from being charged with academic dishonesty.
Even though you are encouraged to work together on homework, letting someone else copy your homework solution is cheating. Supplying help for an in-class assessment is also cheating. Don’t do it.

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.

Policy Against Discrimination, Harassment and Related Interpersonal Violence
The University is committed to maintaining an environment free of discrimination or discriminatory harassment directed toward any person or group within its community – students, employees, or visitors. Academic and professional excellence can flourish only when each member of our community is assured an atmosphere of mutual respect. All members of the University community are responsible for the maintenance of an academic and work environment in which people are free to learn and work without fear of discrimination or discriminatory harassment. In addition, inappropriate amorous relationships can undermine the University’s mission when those in positions of authority abuse or appear to abuse their authority. To that end, and in accordance with federal and state law, the University prohibits discrimination and discriminatory harassment, as well as inappropriate amorous relationships, and such behavior will be met with appropriate disciplinary action, up to and including dismissal from the University. Additionally, to protect the campus community, all non-confidential University employees (including faculty) are required to report sexual assaults, intimate partner violence, and/or stalking involving a student that they witness or are told about to the Office of Institutional Equity. The University takes all reports with the utmost seriousness. Please be aware that while the information you provide will remain private, it will not be confidential and will be shared with University officials who can help. More information is available at equity.uconn.edu and titleix.uconn.edu.
Statement on Absences from Class Due to Religious Observances and Extra-Curricular Activities
Faculty and instructors are expected to reasonably accommodate individual religious practices unless doing so would result in fundamental alteration of class objectives or undue hardship to the University’s legitimate business purposes. Such accommodations may include rescheduling an exam or giving a make-up exam, allowing a presentation to be made on a different date or assigning the student appropriate make-up work that is intrinsically no more difficult than the original assignment. Faculty and instructors are strongly encouraged to allow students to complete work missed due to participation in extra-curricular activities that enrich their experience, support their scholarly development, and benefit the university community. Examples include participation in scholarly presentations, performing arts, and intercollegiate sports, when the participation is at the request of, or coordinated by, a University official. Students should be encouraged to review the course syllabus at the beginning of the semester for potential conflicts and promptly notify their instructor of any anticipated accommodation needs. Students are responsible for making arrangements in advance to make up missed work.For conflicts with final examinations, students should contact the Dean of Students Office. Faculty and instructors are also encouraged to respond when the Counseling Program for Intercollegiate Athletes (CPIA) requests student progress reports. This will enable the counselors to give our students appropriate advice.
Students with Disabilities
The University of Connecticut is committed to protecting the rights of individuals with disabilities and assuring that the learning environment is accessible. If you anticipate or experience physical or academic barriers based on disability or pregnancy, please let me know immediately so that we can discuss options. Students who require accommodations should contact the Center for Students with Disabilities, Wilbur Cross Building Room 204, (860) 486-2020 or http://csd.uconn.edu/.
Emergency Preparedness
In case of inclement weather, a natural disaster, or a campus emergency, the University communicates through email and text message. Students are encouraged to sign up for alerts through http://alert.uconn.edu. Students should be aware of emergency procedures, and further information is available through the Office of Emergency Management at http://publicsafety.uconn.edu/emergency/.