IWoAT 2019

Scientific Committee

Lars Hesselholt, Nagoya University & University of Copenhagen

Peter May, University of Chicago

Lecturers

Meng Guo, Perimeter Institute for Theoretical Physics & University of Toronto

Hana Jia Kong, University of Chicago (Lead)

Nicholas Kuhn, University of Virginia

Ang Li, University of Kentucky

Guchuan Li, Northwestern University

Weinan Lin, University of Chicago

Yunze Lu, University of Michigan

Jonathan Rubin, University of California at Los Angeles

XiaoLin Danny Shi, Harvard University

Haoqing Wu, Swiss Federal Institute of Technology in Lausanne

Mingcong Zeng, Utrecht University

Ningchuan Zhang, University of Illinois at Urbana-Champaign

Foling Zou, University of Chicago

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

Summer School on Equivariant Homotopy Theory