Summer School on Chromatic Homotopy Theory and Higher (Infinity-Categorical) Algebra


This year, the International Workshop on Algebraic Topology (IWoAT) remains a summer school, on the topics of chromatic homotopy theory and higher (infinity-categorical) algebra. This was originally planned for Summer 2020 and is designed to evolve for next installment. This year’s event is jointly sponsored by Shanghai Center for Mathematical Sciences & School of Mathematical Sciences, Fudan University and Yanqi Lake Beijing Institute of Mathematical Sciences and Applications (BIMSA). The two week event will take place fully online from August 15 to August 26, 2022, with details to be announced.


Schedule and Syllabus (updated July 21, 2022)

ZOOM: 388 528 9728, Passcode: BIMSA

Mon. Aug. 15, Day 1

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


Tue. Aug. 16, Day 2

8:30–9:30, Opening talk (to be confirmed)
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)


Wed. Aug. 17, Day 3

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)


Thu. Aug. 18, Day 4

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


Fri. Aug. 19, Day 5

8:30–9:30, Guchuan Li, Lecture 10: Quillen's theorem on π*MU
10:00–11:00, Guchuan Li, Lecture 11: Understand formal groups (over fields)


Mon. Aug. 22, Day 6

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


Tue. Aug. 23, Day 7

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


Wed. Aug. 24, Day 8

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


Thu. Aug. 25, Day 9

8:30–9:30, Yutao Liu, Lecture 19: Construction of vn-self maps
10:00–11:00, Ningchuan Zhang, Lecture 20: Bousfield localizations


Fri. Aug. 26, Day 10

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




Scientific Committee

  • David Gepner, Johns Hopkins University

  • Lars Hesselholt, Nagoya University & University of Copenhagen

  • Gijs Heuts, Utrecht University

  • Jacob Lurie, Institute for Advanced Study




Assistants: Jiao Liu, Fudan University and Siwei Chen, BIMSA



Previous Summer Schools:   2021   2020   2019   2018