This is the webpage of the student learning seminar on Floer Homotopy Theory. The current version of the website design is stolen from the 2017 Seiberg-Witten Seminar.

The seminar is usually held on **4:30-6pm** in room **507**. Sometimes it will be in room **622**; those dates will be announced by email and will be posted in the schedule below.

The goal of this seminar is for it to be leisurely and cover various bits of interesting background. We hope that by the end the participants of the seminar understand how to build maps between floer homotopy types (barring technicalities abound the existence of manifolds-with-corners structures on Floer moduli spaces.)

The first few lectures will cover homotopical basics: spectra, operads.

References:

- [Cohen-Review] Cohen, Floer Homotopy Theory, Revisited (arXiv:1901.08694)
- [CJS] Cohen-Jones-Segal, Floer's Infinite Dimensional Morse Theory and Homotopy Theory
- [Cohen-Cotangent] Cohen, The Floer homotopy type of the cotangent bundle
- [Cohen-Chain-Complexes] Cohen, ... realizing chain complexes by module spectra, ...
- [Schwede] Schwede, Lectures on Equivariant Stable Homotopy theory. (This is an excellent recap of the basics of orthogonal spectra!)
- [Talbot] Notes from 2015 Talbot workshop
- [Rognes] Stable homotopy theory
- [Lipshitz-Sarkar] A Khovanov Homotopy Type
- [LS-Review] Spatial refinements and Khovanov homology

Please e-mail the organizers if you'd like to receive notifications.

**Organizers:** Semon Rezchikov.

THE DATES BELOW ARE NOT COMPLETELY SET IN STONE!

Date | Speaker | Title | Ref. |
---|---|---|---|

March 14th | Semon Rezchikov | Introduction to Stable Homotopy Theory | [Cohen-Review] and Adams' book |

March 28 | Alex Pieloch | Orthogonal Spectra | [Schwede] p. 2-6, [Rognes] |

April 4 | Yash Demukh | Operads | [Talbot] |

April 11 | Semon Rezchikov | Realizing Chain Complexes by Module Spectra | [Cohen-Review] |

April 18 | Semon Rezchikov | The Orientation Problem in Floer Homotopy Theory | [Cohen-Review] |

April 25 | Mohammed Abouzaid | TBA | |

May 2 | Melissa Zhang | The Khovanov Homotopy Type | [Lipshitz-Sarkar], [LS-Review] |

May 9 | Yoel Groman | The Floer Homotopy of the Cotangent Bundle | [Cohen-Cotangent] |