# Junior Chromatic Homotopy Theory Seminar

Max Blans, Sven van Nigtevecht, and I organized the Junior Chromatic Homotopy Theory Seminar 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 0.0****7**

*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****1****0****, 11.00-13.00, in BBG 0.71**

*Heights of formal group laws,*Miguel Barrero*.***December****1****7****, 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 2****8****, 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 t**hick subcategor**y theorem,*Sven van Nigtevecht*.***May 6****, 11.00-13.00, in BBG 0.****6****5***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***Telesc**opic vs. E(n)-localization,*Miguel Barata*.*