### About

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.
The two week event will take place fully online from August 15 to August 26, 2022 at zoom 388
528 9728 with passcode BIMSA.

### Registration

To participate in the online summer school, please fill out a registration form
here.
If you have any questions, please write to Ms. Jiao Liu (刘娇，liujiao@fudan.edu.cn).

Zoom: 388 528 9728

Passcode: BIMSA

All talks will be China Standard Time (GMT+8).

The recordings can be found at the following places.

IWoAT Youtube Channel
IWoAT Bilibili Channel
#### 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**, Chromatic Lecture 1:

*Cohomology theories, Brown representability, K-theory* [notes]
11:00–12:00,

**Heyi Zhu**,

∞-Categories Lecture 1:

*Simplicial sets, Kan complexes, categories, nerves, simplicial categories, infinity
categories, homotopy categories, equivalences* [notes]
#### Tue. Aug. 16, Day 2

8:30–9:30,

**David Gepner**, Opening talk

[notes]
9:45–10:45,

**Sihao Ma**, Chromatic Lecture 2:

*Complex bordism, Thom construction* [notes]
11:00–12:00,

**Heyi Zhu**,

∞-Categories Lecture 2:

*Joins, slices, initial/final objects, limits/colimits, functor categories,
uniqueness (up to contractible space of choices)* [notes]
#### Wed. Aug. 17, Day 3

8:30–9:30,

**Ang Li**, Chromatic Lecture 3:

*Spectra, smash product, ring spectra* [notes]
10:00–11:00,

**Ang Li**,

∞-Categories Lecture 3:

*Left/right fibrations, cartesian/cocartesian fibrations, set up the straightening
functor* [notes]
#### Thu. Aug. 18, Day 4

8:30–9:30,

**Yutao Liu**,Chromatic Lecture 4:

*Complex orientations, formal groups, example of KU* [notes]
9:45–10:45,

**Zhipeng Duan**, Chromatic Lecture 5:

*MU as a universal example,
calculations of MU*_{*}MU and E_{*}MU [notes]
11:00–12:00,

**Yunze Lu**,

∞-Categories Lecture 4:

*Adjoint functors, presentability, tensor product* [notes]
#### Fri. Aug. 19, Day 5

8:30–9:30,

**Guchuan Li**, Chromatic Lecture 6:

*Quillen's theorem on π*_{*}MU [notes]
10:00–11:00,

**Guchuan Li**, Chromatic Lecture 7:

*Understand formal groups (over fields)* [notes]
#### Mon. Aug. 22, Day 6

8:30–9:30,

**Zhipeng Duan**, Chromatic Lecture 8:

*"Higher algebra" (ring spectra and modules), application:
construct K(n), introduce E-theory* [notes]
10:00–11:00,

**Yunze Lu**,

∞-Categories Lecture 5:

*Smash products, stability, stabilization* [notes]
#### Tue. Aug. 23, Day 7

8:30–9:30,

**Hana Jia Kong**,

∞-Categories Lecture 6:

*Derived categories, triangulated categories, t-structures* [notes]
10:00–11:00,

**Weinan Lin**, Chromatic Lecture 9:

*Thick subcategories, define type n, Balmer spectrum of finite spectra, state
thick subcategory theorem* [notes]
#### Wed. Aug. 24, Day 8

8:30–9:30,

**Weinan Lin**, Chromatic Lecture 10:

*Nilpotence theorem, thick subcategory theorem* [notes]
9:45–10:45,

**Foling Zou**,

∞-Categories Lecture 7:

*Monoidal and symmetric monoidal structures* [notes]
11:00–12:00,

**Foling Zou**,

∞-Categories Lecture 8:

*Rings (associative and commutative) and modules* [notes]
#### Thu. Aug. 25, Day 9

8:30–9:30,

**Yutao Liu**, Chromatic Lecture 11:

*Construction of v*_{n}-self maps [notes]
10:00–11:00,

**Ningchuan Zhang**, Chromatic Lecture 12:

*Bousfield localizations* [notes]
#### Fri. Aug. 26, Day 10

8:30–9:30,

**Ningchuan Zhang**, Chromatic Lecture 13:

*Monochromatic layers, chromatic convergence theorem* [notes]
10:00–11:00,

**Hana Jia Kong**,

∞-Categories Lecture 9:

*The Barr-Beck-Lurie theorem* [notes]
11:00–11:10,

**Jie Wu**, Closing remarks

### Lecturers

Zhipeng Duan, Nanjing Normal University
Hana Jia Kong, Institute for Advanced Study
Ang Li, University of California, Santa Cruz
Guchuan Li, University of Michigan
Weinan Lin, Peking University
Yutao Liu, University of Chicago
Yunze Lu, University of California San Diego
Sihao Ma, University of Notre Dame
Ningchuan Zhang, University of Pennsylvania
Heyi Zhu, University of Illinois Urbana-Champaign
Foling Zou, University of Michigan
### Scientific Committee

David Gepner, Johns Hopkins University
Lars Hesselholt, Nagoya University & University of Copenhagen
Gijs Heuts, Utrecht University
Jacob Lurie, Institute for Advanced Study
### Organizers

Hana Jia Kong, Institute for Advanced Study
Zhi Lü, Fudan University
Peter May, University of Chicago
XiaoLin Danny Shi, University of Washington
Guozhen Wang, Fudan University
Jie Wu, BIMSA
Zhouli Xu, University of California San Diego
Yifei Zhu, Southern University of Science and Technology

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