Homological Algebra

This reading course offers a comprehensive introduction to homological algebra, blending foundational theory with practical tools. We plan to follow chapters 1-5 and 10 from ‘An introduction to Homological Algebra‘ by Charles Weibel. The course assumes familiarity with algebra and category theory, and will first explore the structure of abelian categories, injective and projective objects, and spectral sequences. We will then look at applications in sheaf cohomology, group cohomology, and Hochschild cohomology, equipping us with essential computational techniques. Advanced topics include derived and dg categories, and simplicial objects, culminating in a discussion of the Dold–Kan correspondence. By the end of the course, participants will have gained an understanding of homological methods, and be able to apply them in their academic progress.

When: Tuesdays 16-18

Organizer: Alexandra Ciotau