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|