Mathematics 797E - ST-Homological Algebra

Homological algebra can be seen as a generalization and extension of linear algebra, and so it plays an essential role in many areas of contemporary mathematics. Like linear algebra, it is important to understand both algorithms but also powerful structural results, and we will give due attention to both aspects. This course will lay foundations in a way guided by modern views (e.g., we will introduce model categories) but will also explore classic applications, like group cohomology and Lie algebra cohomology, so that computational facility is developed. By the end of the course, you will know what a derived category is and how to run a spectral sequence.

Math 611 and preferably Math 612 as well. Some exposure to algebraic topology or algebraic geometry would be helpful but is not necessary.