Ämnesdisposition

  • Course description

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    This is a supervised reading course for Master students who want to learn about stable homotopy theory. The goal is to cover most of chapters 2 - 6 in Cary Malkiewich's draft textbook.

    The course will take place during June and August 2025, with a bit of spillover into the first weeks of July and September. We will meet roughly once a week. Alexander and Greg will take turns leading the meetings. 

    The planned format is that every meeting will start with a presentation by one or two of you on the material you have read last week, followed by questions and discussion. Please write to Alexander or Greg if you want to volunteer for a presentation on a certain week.

    There is an option to follow the meetings by Zoom

    Meeting ID: 683 0495 8305
    Passcode: 168592

    (This service is offered as is, no guarantee of quality.)

    The following is a tentative schedule of meetings. Unless otherwise said, all meetings take place from 10:15-12:00 in Cramer room. Note that things may change and probably will.


    Course plan
    Day                      Supervisor           Material                                                                                       Sections to read beforehand       Remarks
    June 10 Greg Definition of spectra, stability theorem 2.1-2.4 This is Tuesday. All others are planned to be on Thursday
    June 12 Alexander Generalised (co)homology theories, Brown representability theorem. 2.5-2.6. See also 1.4.3 Two meetings on our first week.
    June 19 Greg The stable homotopy category 3.1-3.2
    June 26 No meeting, because of the YTM
    July 3 Alexander Functors on the homotopy category. Derived functors 3.3-3.4
    July 4 - Aug 10 Summer vacation
    Aug 14 Greg Smash product on the homotopy category, duality 4.1-4.2
    Aug 21 Alexander Model categories 1 - general theory 5.1-5.4
    Aug 28 Greg Model categories 2 - Spectra, Bousfield localization 5.5-5.7
    Sep 4 Alexander Constructing rigid smash product of spectra 6.1-6.4


    The grade will be determined by an oral exam and at least one homework assignment. Active participation in discussions can help boost the grade in borderline cases :-)