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色同伦论与高阶(无穷范畴)代数暑期学校下周开课

来源: 08-15

时间: 15- 26 August 2022

地点:ZOOM: 388 528 9728 PASSWORD: BIMSA

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

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