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!"


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


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:

For Spectra and E_∞-rings, and operads:

For localizations of Spectra

For an Intro to Chromatic Homotopy theory: