MAT 607, Fall 2017

Welcome to Math 607, Homological Algebra. The syllabus is here.

This website will be used to make announcements, post homework assignments, etcetera.

Office hours are Monday and Wednesday at 10AM.

I'm going to try a new approach to homework. This is a topics course and often this means people don't do the homework (often for lack of time and too much inertia). However, I am a firm believer that without doing exercises you will not acquire tools (and will eventually fall behind in the class too). So, I will try to assign one short exercise per day (less than half an hour of work, especially if worked in groups), expecting it to be done before the next class.
It's also a topics course, so your grade is almost entirely irrelevant. But some people like carrots, so your grade for the course will be dependent entirely on the homework done. See the syllabus for details.

We will mostly be working from Weibel's book An Introduction to Homological Algebra. You can find a pdf online if you look, but this is an excellent reference so it is worth buying. Some topics will be taken from other books, such as MacLane's Categories for the Working Mathematician which is also a recommended purchase. If you seek monetary assistance in buying books, let me know.

Crawley-Boevey's lecture notes on quivers can be found here.

A portion of a good intro to derived categories and t-structures can be found here.

I will keep one file with the exercises, and will update it periodically. It is here. It contains recommended reading.

I have a pdf with my notes from last time I taught the course, but I think I will make a new pdf with course notes, in an attempt to fix various errors and improve the curriculum. So expect this to be posted online soon as well.
More accurately, I've started making complete notes somewhere in the middle of the class, so here they are, sorted by topic.
Homological dimension
More on Koszul complexes
Ext and extensions, the Yoneda product
Stuff on Cones
Triangulated categories and the definition of derived categories

My teaching aid for the octahedral axiom. The vertices represent objects (up to shift), and the edges maps (there is some orientation). The solid triangles are commutative, while the hollow triangles are distinguished. The solid square is commutative. The outer square (with attempted green highlighting) is anticommutative! (The third square is oriented cyclically.)

Ben Elias
Department of Mathematics
Fenton Hall, Room 210
University of Oregon
Eugene, OR 97403
Phone: (541) 346-5629
Fax: (541) 346-0987