Stable homotopy theory is the study of spectra: homotopical versions of abelian groups. While traditionally seen as a subfield of algebraic topology, techniques from stable homotopy theory are becoming increasingly important in various neighboring fields.
In the course, we will:
1) Introduce the formalism of oo-categories,
2) Introduce stable oo-categories and the oo-category of spectra
3) Prove May's recognition principle for connective spectra
4) Study homological algebra via derived oo-categories
5) Study examples of spectra, like topological K-theory, and techniques like localizations and completions.
Lectures: Monday, 16:15-17:45, M102 and Wednesday, 10:15-11:45, M102.
Exercise sessions: Thursday, 14:15-15:45, M009.
I will also live-stream the lectures on Zoom.
The lectures will be based on my in-progress text book Stable Homotopy Theory and Higher Algebra .