MAT 536 Course Webpage Algebra III: Homological and Homotopical Algebra Tu Th 2:30PM — 3:50PM, Library W4530 Fall 2015

Course Announcements Announcements about the course will be posted here. Please check the site regularly for announcements (which will also be given in lecture).

Course Description This course will begin with a review of the construction of Ext and Tor. Then we will study the construction of general derived functors, spectral sequences, etc. We will proceed to study triangulated categories and total derived functors. With the remaining time, there will be a discussion of simplicial methods as in the construction of the André-Quillen homology / cohomology.

Prerequisites Students should have passed the graduate algebra sequence. Some of the main examples will use the language of sheaves, so that is also quite useful.

Text There is no required textbook. The following are excellent reference for homological algebra.

• Charles Weibel, An Introduction to Homological Algebra, Cambridge University Press.
• Sergei Gelfand and Yuri Manin, Methods of Homological Algebra, Springer.

• A. J. de Jong, et al., The Stacks Project.
• Paul Goerss and John Jardine, Simplicial Homotopy Theory, Birkhäuser.
• Daniel Quillen, Homotopical Algebra, Springer.

Lectures The instructor for this course is Jason Starr. All instruction will occur in lectures. A tentative schedule will be posted in the syllabus.

Lecture is held Tuesdays and Thursdays, 2:30 PM — 3:50PM in Library W4530.

Office Hours Office hours are Tuesdays, 1 PM — 2 PM, and Thursdays, 1 PM — 2 PM in Math Tower 4—108. I also do advising on Tuesdays, 11 AM — 12 NOON in Math Tower P—143.

Grading System As will be discussed at the first class meeting, grading will be based on class participation and problem sets.

Disability Support Services If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, 128 ECC Building (631) 632-6748. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following web site: http://www.ehs.sunysb.edu and search Fire Safety and Evacuation and Disabilities.

Academic Integrity Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instance of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/.

Critical Incident Management Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, and/or inhibits students' ability to learn.

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