In Fall 2018, the homotopy theory learning seminar is on families of elements in the stable ho­motopy groups of the spheres, following Ravenel's green book [Rav86]. This seminar is organized by Arun Debray and Richard Wong.

Schedule:

Planning meeting and overview

Richard, September 5

Introduction to spectra

Rok, September 10

Spectral sequences: construction and use

Ricky and Arun, September 17

The Adams and Adams-Novikov spectral sequences

Riccardo, Alberto, and Richard, September 24, October 1, and October 8
[Rav86] §§2.2, 4.4

Construction of BP and MU

Ty, October 22

Hopf algebroids

Rok, October 29

Some calculations with BP_*BP

Riccardo, November 5
[Rav86] §4.3

First calculations with the Adams-Novikov spectral sequence

Arun, November 12
[Rav86] §4.4

Greek letter elements, etc.

Richard, November 19
[Rav86] §5.1

Hopf invariant one

Arun, Riccardo, and Alberto, November 26 and December 3
[Rav86] §5.2

The image of J

Rok, Ty, and Ricky (possibly), December 10
[Rav86] §5.3

Main references:

[Rav86]

Douglas C. Ravenel, Complex Cobordism and Stable Homotopy Groups of Spheres.

Related links:

[BC18]

Agnès Beaudry and Jonathan Campbell, “A Guide for Computing Stable Homotopy Groups.”

[Rog12]

John Rognes, “The Adams spectral sequence.”