Schedule
08-15
8:20-8:30
Guozhen Wang
Opening remarks
8:30-9:30
Jacob Lurie
Opening talk
9:45-10:45
Sihao Ma
Lecture 1: Cohomology theories, Brown representability, K-theory
11:00-12:00
Heyi Zhu
Lecture 2: Simplicial sets, Kan complexes, categories, nerves, simplicial categories, infinity categories, homotopy categories, equivalences
08-16
8:30-9:30
David Gepner
Opening talk
9:45-10:45
Sihao Ma
Lecture 3: Complex bordism, Thom construction
11:00-12:00
Heyi Zhu
Lecture 4: Joins, slices, initial/final objects, limits/colimits, functor categories, uniqueness (up to contractible space of choices)
08-17
8:30-9:30
Ang Li
Lecture 5: Spectra, smash product, ring spectra
10:00-11:00
Ang Li
Lecture 6: Left/right fibrations, cartesian/cocartesian fibrations, set up the straightening functor (or at least state the theorem), stacks as an example (Hopf algebroids)
08-18
8:30-9:30
Yutao Liu
Lecture 7: Complex orientations, formal groups, example of KU
9:45-10:45
Zhipeng Duan
Lecture 8: MU as a universal example (viewed as moduli stack, see Lecture 6), calculations of MU*MU and E*MU
11:00-12:00
Yunze Lu
Lecture 9: Adjoint functors, presentability, tensor product
08-19
8:30-9:30
Guchuan Li
Lecture 10: Quillen's theorem on π*MU
10:00-11:00
Guchuan Li
Understand formal groups (over fields)
08-22
8:30-9:30
Zhipeng Duan
Lecture 12: "Higher algebra" (ring spectra and modules, see Lecture 18), application: construct K(n), introduce E-theory
10:00-11:00
Yunze Lu
Lecture 13: Smash products (see Lecture 5), stability, stabilization
08-23
8:30-9:30
Hana Jia Kong
Lecture 14: Derived categories, Verdier sequences, t-structures
10:00-11:00
Weinan Lin
Lecture 15: Thick subcategories, define type n, Balmer spectrum of finite spectra, state thick subcategory theorem
08-24
8:30-9:30
Weinan Lin
Lecture 16: State nilpotence theorem, deduce thick subcategory theorem
9:45-10:45
Foling Zou
Lecture 17: Monoidal and symmetric monoidal structures
11:00-12:00
Foling Zou
Lecture 18: Rings (associative and commutative) and modules
08-25
8:30-9:30
Yutao Liu
Lecture 19: Construction of vn-self maps
10:00-11:00
Ningchuan Zhang
Lecture 20: Bousfield localizations
08-26
8:30-9:30
Ningchuan Zhang
Lecture 21: Monochromatic layers, chromatic convergence theorem
10:00-11:00
Hana Jia Kong
Lecture 22: The Barr-Beck-Lurie theorem
11:00-11:10
Jie Wu
Closing remarks
