**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 v_{n}-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