Chromatic Homotopy Theory

We are pleased to announce a new seminar series on chromatic homotopy theory. The main speaker will be Clark Barwick, with the hope that participants will contribute talks later in the series.

"The chromatic filtration on the stable homotopy groups of spheres is a reflection of the height filtration on the moduli stack of commutative, 1-dimensional formal group laws. Taking this idea seriously means forging a link between arithmetic geometry and homotopy theory. Periodicity phenomena deep within stable homotopy theory reflect structures found on the moduli stack of formal groups (or, perhaps better, p-divisible groups).

Many special objects in mathematics meet in chromatic homotopy theory: complex orientations, the Adams-Novikov spectral sequence, formal groups, p-divisible groups, modular forms, and even (conjecturally) certain quantum field theories. One theme I'll be particularly enthused about is using the Fargues-Fontaine curve to reimagine the geometry controlling the chromatic filtration.

I'm eager to give many of the talks, but eventually topics will arise that others are likely to understand better. Please volunteer!"

Schedule

We meet every Tuesday at 10:30-12:30, with the first hour reserved for a talk and the second hour reserved for open discussion.

For weekly reminders and room updates, please sign up to the mailing list.

Date	Room	Speaker	Topic	Recording
Jan 31	Bayes 5.02	Clark Barwick	Introduction and overview
Feb 7	JCMB 5323	Clark Barwick	Spectra	Recording link
Feb 14	JCMB 5323	Clark Barwick	Localisations	Recording link
Feb 21	JCMB 5323	Clark Barwick	Bousfield localisation	Recording link
March 14	JCMB 5323	Clark Barwick	Discussion	March 21	JCMB 5323	Clark Barwick	Formal groups	Recording link
...
May 2	JCMB 5323	Malthe Sporring	The Adams Spectral Sequence
May 9	JCMB 5323
May 16	JCMB 5323
May 23	JCMB 5323
May 30	JCMB 5323

Notes

The notes are available here, typed by Willow Bevington and Malthe Sporring, from whom all the mistakes in the notes will originate.

Recommended References

For ∞-categories:

Land "An intro to ∞-categories"
Lurie "Higher Topos Theory"

For Spectra and E_∞-rings, and operads:

Nardin "Introduction to Stable Homotopy Theory"
Segal "Categories and Cohomology theories"
Lurie "Higher Algebra"

For localizations of Spectra

Bousfield, Kan "Homotopy limits, completions and localizations" (1972)
Bousfield "The localization of spectra with respect to homology" (1979)
Bauer "Bousfield localization and the Hasse square" (2011)
VanKoughnett "Spectra and localization" (2013)
Douglas, Francis, Henriques, Hill (eds.) "Topological Modular Forms" (2014)
Riehl "Categorical homotopy theory" (2014)
Lawson "An Introduction to Bousfield Localization"

For an Intro to Chromatic Homotopy theory:

Ravenel "Complex Cobordism and stable homotopy groups of spheres"
Hopkins "Complex oriented cohomology theories and the language of stacks"