jCHTS (2021-2022)

Max Blans, Sven van Nigtevecht, and I organized the Junior Chromatic Homotopy Theory Seminar (jCHTS) where we covered the basic notions of chromatic homotopy theory, following Lurie's lecture series [1] on this matter. The seminar is aimed at starting PhD students, but interested master students familiar with the basics of stable homotopy theory are also welcome to join. Please drop me an e-mail if you would like to come to our seminar meetings!

Time & location

The seminar will take place every Friday from 11.00-13.00. The location may change from time to time, see the schedule below.

References

[1] Jacob Lurie. Chromatic homotopy theory. Lecture notes. (An overview of the lecture titles can be found here and possible elucidations of the material can be found in the lecture notes written by Christopher Schommer-Pries for the same course).
[2] Piotr Pstrągowski. Finite height chromatic homotopy theory. Lecture notes.
[3] Lennart Meier. Elliptic homology and topological modular forms. Lecture notes.
[4] Michael Hopkins. Complex oriented cohomology theories and the language of stacks. Lecture notes.
[5] Sanath Devalapurkar. Chromatic homotopy theory. Lecture notes.

Schedule

Part I: Formal group laws and complex-oriented cohomology theories

October 1, 11.00-13.00, in HFG 6.10
Introduction & Lazard's theorem, Max Blans.
October 8, 11.00-13.00, in HFG 6.10
The symmetric cocyle lemma, Sven van Nigtevecht.
October 15, 11.00-13.00, in HFG 6.10
Complex-oriented cohomology theories, Miguel Barata.
October 22, 11.00-13.00, in HFG 6.10
The complex bordism spectrum, Miguel Barrero.

Part II: Quillen's theorem

October 29, 11.00-13.00, in HFG 6.10
The homology of MU, Jaco Ruit.
November 5, 11.00-13.00, in Minnaert 2.06
A short intermezzo on stacks, Sven van Nigtevecht. Sven's lecture notes.
November 12, 11.00-13.00, in BBG 0.07
The Adams spectral sequence, Max Blans.
November 19, 11.15-13.15, in HFG 6.10
The proof of Quillen's theorem, Miguel Barata.

Part III: The moduli stack of formal groups

November 26, 11.00-13.00, in BBG 0.77
Formal groups, Jack Davies.
December 3, 11.00-13.00, in BBG 0.05
Stacky intermezzo II: Quasi-coherent sheaves on stacks, Sven van Nigtevecht. Sven's lecture notes.
December 10, 11.00-13.00, in BBG 0.71
Heights of formal group laws, Miguel Barrero.
December 17, 11.00-13.00, in BBG 0.71
The height filtration of the moduli stack of formal groups, Jaco Ruit.
Christmas break 🎄
January 14, 11.00-13.00, online via Teams
The classification of formal group laws, Max Blans. Max' lecture notes.
January 21, 11.00-13.00, in BBG 0.69
The Morava stabilizer groups, Yuqing Shi.

Part IV: The Landweber exact functor theorem

January 28, 11.00-13.00, in BBG 0.69
Flat modules over the moduli stack of formal groups, Miguel Barata.
February 4, 11.00-13.00, in BBG 0.69
The Landweber exact functor theorem, Jaco Ruit.
February 11, 11.00-13.00, in BBG 0.79
Phantom maps of spectra, Ryan Quinn.
February 25, 11.00-13.00, in Minnaert 2.05
Even periodic cohomology theories, Sven van Nigtevecht.

Part V: The Morava E- and K-theories

March 4, 11.00-13.00, in Minnaert 2.05
Bousfield localizations, Yuqing Shi.
March 11, 11.00-13.00, in Minnaert 2.05
Lubin-Tate theory, Max Blans.
March 25, 11.00-13.00, in Minnaert 2.05
The Morava E- and K-theories, Jaco Ruit.
April 1, 11.00-13.00, in Minnaert 2.05
The Bousfield classes of the Morava E- and K-theories, Jack Davies.
April 8, 11.00-13.00, in Minnaert 2.05
The uniqueness of Morava K-theory, Miguel Barata.

Part VI: The periodicity theorem

April 22, 11.00-13.00, in BBG 0.05
The nilpotence theorem, Sven van Nigtevecht.
April 29, 11.00-13.00, in BBG 0.05
The thick subcategory theorem, Sven van Nigtevecht.
May 6, 11.00-13.00, in BBG 0.65
The periodicity theorem, Max Blans.

Part VII: The telescope conjecture

May 13, 11.00-13.00, in BBG 0.65
Telescopic localization, Jaco Ruit.
June 3, 11.00-13.00, in BBG 0.65
Telescopic vs. E(n)-localization, Miguel Barata.