The course Homotopical algebra (with a view towards derived algebraic geometry) will be held at SISSA, on Tuesday, 9-11 am and on Wednesday, 2-4pm, starting from March 25th, 2025. The notes and the topics for each lecture will be collected here.
The schedule and rooms for each lecture are as follows. (Please note the room changes!)
Tuesday March 25, 2025, 9:00-11:00, Room 136.
Topic: Introduction to model categories. (Notes)Wednesday March 26, 2025, 14:00-16:00, Room 133.
Topic: Interaction between homotopy theories. (Notes)Tuesday April 1, 2025, 9:00-11:00, Room 136.
Topic: ∞-category theory. (Notes)Wednesday April 2, 2025, 14:00-16:00, Room 133.
Topic: Grothendieck construction; stable ∞-categories. (Notes)Tuesday April 8, 2025, 9:00-11:00, Room 136.
Topic: The stable ∞-category of spectra. (Notes)Wednesday April 9, 2025, 14:00-16:00, Room 133.
Topic: Rings and modules in the stable ∞-category. (Notes)Tuesday April 15, 2025, 9:00-11:00, Room 134.
Topic: Algebra in the stable ∞-category. (Notes)Wednesday April 16, 2025, 14:00-16:00, Room 133.
Topic: Cotangent complex and square-zero extensions. (Notes)Tuesday April 22, 2025, 09:00-11:00, Room 134.
Topic: Introduction to spectral (pre)stacks. (Notes)Wednesday April 23, 2025, 14:00-16:00, Room 133.
Topic: Distinguished class of derived stacks; quasi-coherent sheaves. (Notes)
Some auxiliary readings.