Math 9501A: Homotopical Algebra
Essential information
- Lectures: [information available only to enrolled students]
- Office hours: by appointment
- Instructor: Chris Kapulkin
- Email: kkapulki (at) uwo.ca
- Office: MC 255C
- Website: http://uwo.ca/math/faculty/kapulkin/courses/2023-9501A.html
- Prerequisites: Math 9052/4152 (Algebraic Topology) and Math 9511 (Category Theory), or permission of instructor.
Textbook
We will cover a selection of topics from
- D.-C. Cisinski, Higher Categories and Homotopical Algebra, 2019.
- M. Hovey, Model Categories, 1999.
Course content
The topics will include:
- Model categories and homotopy theory therein, Quillen functors and equivalences
- Examples of model categories, including topological spaces and chain complexes
- Simplicial sets: the Kan-Quillen and Joyal model structures
- Introduction to ∞-categories
Evaluation
The final grades will be based on the following components:
- ten weekly assignments: 50%
- tutorial presentations: 15%
- final project: 15%
- final presentation: 20%
Tutorials
Each week, there will be a one-hour tutorial instead of a regular lecture. One week prior to the tutorial, the instructor will distribute a list of 5 problems assigning three of them to specific students (taking into account students' input and preferences). The students will then present their solutions during the tutorial. The remaining two problems will be be solved by all students in writing and the solutions will be submitted via Gradescope prior to the tutorial.
Each student shall present solutions to at least three problems during the term. The solutions will be graded on the scale 0-5 with a maximum of 3 points for correctness and 2 points for clarity of presentation.
Each written submission will also be graded on the scale 0-5, taking into account both correctness of the solution and clarity of the exposition. Solutions need to be typeset in LaTeX; handwritten solutions will not be accepted.
Project/Presentation
As part of the evaluation, each student will need to write a 10-15 page long document in LaTeX, surveying a topic in homotopical algebra. The instructor will prepare a list of recommended projects, but students are welcome and in fact encouraged to suggest their own topics.
Associated with the project, each student will be required to give a 30-minute presentation during the last week of the course. The presentations cannot use slides, must include a theorem, and a proof of at least one short lemma.
Accommodation and Accesibility
If you are unable to meet a course requirement due to illness or other serious circumstances, you must provide valid medical or supporting documentation to the Academic Counselling Office of your home faculty as soon as possible. If you are a Science student, the Academic Counselling Office of the Faculty of Science is located in WSC 140, and can be contacted at scibmsac@uwo.ca.
For further information, please consult the university’s medical illness policy at
http://www.uwo.ca/univsec/pdf/academic_policies/appeals/accommodation_medical.pdf.
If you miss the Final Exam, please contact your faculty’s Academic Counselling Office as soon as you are able to do so. They will assess your eligibility to write the Special Exam (the name given by the university to a makeup Final Exam). You may also be eligible to write the Special Exam if you are in a “Multiple Exam Situation”
http://www.registrar.uwo.ca/examinations/exam_schedule.html
Academic Policies
The website for Registrarial Services is http://www.registrar.uwo.ca.
In accordance with policy, http://www.uwo.ca/its/identity/activatenonstudent.html, the centrally administered e-mail account provided to students will be considered the individual’s official university e-mail address. It is the responsibility of the account holder to ensure that e-mail received from the University at his/her official university address is attended to in a timely manner.
Scholastic offences are taken seriously and students are directed to read the appropriate policy, specifically, the definition of what constitutes a Scholastic Offence, at this website:
http://www.uwo.ca/univsec/pdf/academic_policies/appeals/scholastic_discipline_undergrad.pdf.
Student Accessibility Services
Western is committed to achieving barrier-free accessibility for all its members, including graduate students. As part of this commitment, Western provides a variety of services devoted to promoting, advocating, and accommodating persons with disabilities in their respective graduate program.
Graduate students with disabilities (for example, chronic illnesses, mental health conditions, mobility impairments) are encouraged to register with Student Accessibility Services, a confidential service designed to support graduate and undergraduate students through their academic program. With the appropriate documentation, the student will work with both SAS and their graduate programs (normally their Graduate Chair and/or Course instructor) to ensure that appropriate academic accommodations to program requirements are arranged. These accommodations include individual counselling, alternative formatted literature, accessible campus transportation, learning strategy instruction, writing exams and assistive technology instruction.
