Spring 2025 - MATH 894 G100

Reading (2)

Homological Algebra

Class Number: 2763

Delivery Method: In Person

Overview

  • Course Times + Location:

    Location: TBA

  • Instructor:

    Nathan Ilten
  • Instructor:

    Nathan Ilten
    nilten@sfu.ca
    1 778 782-9887

Description

COURSE DETAILS:

Homological Algebra

Spring 2025

Instructor: Nathan Ilten
Thursdays 3:00-4:20 in K9509
2-credit reading course

The class will meet weekly for 80 minutes; 50 minutes will be a presentation by one of the students on the topic of the week, and 30 minutes will be a discussion of homework problems. Each student will be required to present at least twice in class. Prior to each presentation, the student must submit a written outline of their talk. Outlines and presentations will be graded on completeness, correctness and accuracy, and appropriateness for the audience.

Topics to be covered:

• chain complexes
• free, projective, and injective resolutions
• (right/left) exact functors
• derived functors
• Ext and Tor
• Spectral sequences
• Double complexes and associated spectral sequence
• Hilbert’s syzygy theorem
• Grothendieck’s spectral sequence

COURSE-LEVEL EDUCATIONAL GOALS:

Develop basic tools from homological algebra as used in algebra and algebraic geometry.

Grading

  • Completion of homework and participation in homework discussion 10%
  • Presentation outlines 30%
  • Presentations 60%

REQUIREMENTS:

Math 817 and 818 recommended. At a minimum, students should be familiar with rings and modules and localization. Some knowledge of sheaves recommended but not strictly necessary. Registration possible only after discussion with instructor to ensure adequate background.

Materials

MATERIALS + SUPPLIES:

Eisenbud, Commutative Algebra with a view towards algebraic geometry,
appendix 3

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html

RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.