A course on chromatic homotopy theory, January 16 -- February 2, 2018


This is the webpage for the IAP/January course on chromatic homotopy theory, which will be running from January 16 -- February 2, 2018. I had originally planned to start on the 8th, but I will be in San Diego for JMM then.

The official course listing is here. The times listed there are flexible, so please email me at sanathd[at]mit[dot]edu to discuss what times work.

Topics to be covered will include: (basic computations with) the Adams(-Novikov) spectral sequence, the Ravenel conjectures, Morava K- and E-theories, and (if there's time) the construction of TMF. I will be writing lecture notes for every lecture.

Update: we may not be meeting at 2-3 pm as listed on the IAP website; instead, we'll decide the meeting time based on the outcome of this Doodle poll. See below for meeting times!

Update 2: We will be meeting in room 2-361, unless indicated otherwise below.

Update 3: By popular demand, I wrote up some problems. See this link; some of the problems don't have much to do with chromatic homotopy theory, but still give good intuition.

Lecture notes: I have compiled notes from all the lectures into a single document, which you can find here.

The following is an ambitious schedule for this course:

Lecture 1: An overview, and an introduction to the Ravenel conjectures January 16, 4-5 pm in room 2-255 (not 2-361)
Lecture 2: The thick subcategory theorem (lecture by Robert Burklund) January 17, 2-3 pm
Lecture 3.i: Periodicity in stable homotopy theory January 18, 2-3 pm
Lecture 3.ii: Periodicity in stable homotopy theory, continued January 19, 2-3 pm
The smashing conjecture and chromatic convergence (no lecture). N/A
Lecture 4.i: Nilpotence January 22, 4-5 pm
No lecture January 23
Lecture 4.ii: Nilpotence, continued January 24, 4-5 pm
Lecture 5: Landweber exactness January 25, 4-5 pm
Lecture 6.i: Morava E-theories and the K(n)-local sphere January 26, 4-5 pm
Lecture 6.ii: Morava E-theories and the K(n)-local sphere January 29, 4-5 pm
Lecture 7: Stacks (lecture by Miguel Young) January 30, 4-5 pm
No lecture January 31
No lecture February 1 (conflict with Thursday seminar)
Lecture 8: The moduli stack of elliptic curves and TMF February 2, 4-5 pm


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