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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

    Exercises and Open Problems in Equivariant Homotopy Theory (updated August 17, 2019)