### Scientific Committee

### Lecturers

### Syllabus and Schedule

#### Syllabus

All lectures including evening sessions take place in the Gu Lecture Hall, Room 220 of the Shanghai Center for Mathematical Sciences.#### Tue. Aug. 13, Day 1: Nonequivariant background

**[Notes]**9:00–10:20,

**Yunze Lu**, Lecture 1:

*Basic homotopy theory review*

**[Notes]**10:50–12:10,

**Yunze Lu**, Lecture 2:

*Cohomology theories and naive spectra*

**[Notes]**14:00–15:20,

**Foling Zou**, Lecture 3:

*Basics of spectra*

**[Notes]**15:50–17:10,

**Foling Zou**, Lecture 4:

*Monoidal structures*

19:00, Evening session:

*Basic introduction to ∞-categories*

#### Wed. Aug. 14, Day 2: Equivariant homotopy theory

**[Notes]**9:00–10:20,

**Meng Guo**, Lecture 5:

*Equivariant spaces*

**[Notes]**10:50–12:10,

**Hana Jia Kong**, Lecture 6:

*Presheaves on orbit category*

**[Notes]**14:00–15:20,

**Weinan Lin**, Lecture 7:

*Application*

**[Notes]**15:50–17:10,

**Ang Li**, Lecture 8:

*Equivariant spheres, Freudenthal Suspension Theorem and the category of naive spectra*

19:00, Evening session:

*Homology of symmetric groups, the Barratt–Priddy theorem*

#### Thu. Aug. 15, Day 3: Equivariant stable homotopy theory

**[Notes for Lecs. 9 & 11]**9:00–10:20,

**Haoqing Wu**, Lecture 9:

*Introduction to equivariant stable homotopy theory*

**[Notes]**10:50–12:10,

**Jonathan Rubin**, Lecture 10:

*Equivariant spectra and Mackey functors*

14:00–15:20,

**Haoqing Wu**, Lecture 11:

*Orthogonal spectra*

**[Notes]**15:50–17:10,

**Weinan Lin**, Lecture 12:

*Application*

19:00, Evening session:

*Homological algebra of Mackey functors, equivariant cohomology of a point*

#### Fri. Aug. 16, Day 4: Advanced topics

**[Notes]**9:00–10:20,

**Ningchuan Zhang**, Lecture 13:

*Equivariant K-theory*

**[Notes]**10:50–12:10,

**Ningchuan Zhang**, Lecture 14:

*Equivariant cobordism*

**[Notes for Lecs. 15 & 16]**14:00–15:20,

**XiaoLin Danny Shi**, Lecture 15:

*Introduction to HHR*

15:50–17:10,

**XiaoLin Danny Shi**, Lecture 16:

*The slice spectral sequence*

19:00, Evening session

#### Sat. Aug. 17, Day 5: Advanced topics (continued)

**[Notes for Lecs. 17 & 18]**9:00–10:20,

**Mingcong Zeng**, Lecture 17:

*The Slice Differential Theorem, the Periodicity Theorem and the Homotopy Fixed Point Theorem*

10:50–12:10,

**Mingcong Zeng**, Lecture 18:

*The Slice Differential Theorem, the Periodicity Theorem and the Homotopy Fixed Point Theorem (continued)*

**[Notes]**14:00–15:00,

**Guchuan Li**, Lecture 19:

*The Detection Theorem*

**[Notes]**15:20–16:20,

**Guchuan Li**, Lecture 20:

*The Detection Theorem (continued)*

16:40–17:40,

**Nick Kuhn**, Special Lecture:

*An introduction to the Balmer spectrum of G-equivariant finite spectra*