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.

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

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

- 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"

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