Time: 13:30-15:55, Every Thursday of Spring 2025 Semester
Venue: E10-315
Speaker: Lifan Guan
Course Description:
The course is designed to provide an introduction to the theory of sheaves and their cohomology theory from a modern perspective, via the theory of infinity categories.
We will first give the basic definitions of sheaves and the classical six-functors formalism, which is at the heart of the study of sheaf theory. Latter, we will give a quick tour about how to think and use the theory of infinity categories as a blackbox. In particular, we will try to convice the audience, why the stable infinity categories, compared to triangulated categories, provide a much better foundation for homological algebra. Then we move to the modern treatment of the six-functors formalism, which makes an essential use of the theory of infinity categories.
Prerequisite: category theory, homological algebra, knowledge of algebraic geometry will be helpful, but not a must.
