### SoSe 22 Oberseminar: Tempered cohomology and equivariant elliptic cohomology

**Time and place:** Tuesday 14:15-15:45 in M311 and online

Tempered cohomology is a global equivariant cohomology theory associated with a p-divisible group over an E-infinity-ring, which provides higher-chromatic generalizations of equivariant topological K-theory. It is a unifying framework connecting all of the following concepts: p-divisible groups and formal groups, global equivariant homotopy theory, the Atiyah–Segal completion theorem, and the classical and chromatic character theory of finite groups.

The goal of this seminar is to learn the basics of tempered cohomology following Jacob Lurie’s *Elliptic Cohomology III*. We will also review some of the theory of spectral elliptic curves (whose associated tempered cohomology is equivariant elliptic cohomology) and Lurie’s construction of the E-infinity-ring of topological modular forms. Some working knowledge of higher category theory and E-infinity-ring spectra will be assumed.

Date | Speaker | Topic |
---|---|---|

03.05 | Denis Nardin | Introduction |

10.05 | Denis Nardin | Spectral algebraic geometry |

17.05 | Toni Annala | Spectral formal groups |

24.05 | Niklas Kipp | Orientations and Quillen formal groups |

31.05 | Luca Pol | Barsotti–Tate groups |

07.06 | Denis Nardin | The construction of elliptic cohomology |

14.06 | Marco Volpe | Orbispaces and equivariant homotopy theory |

21.06 | Marc Hoyois | The tempered cohomology associated to a preorientation |

28.06 | Massimo Pippi | Equivariant K-theory as tempered cohomology |

05.07 | Luca Pol | The Atiyah–Segal comparison map |

12.07 | Lucy Yang | The character map for tempered cohomology |

19.07 | Marc Hoyois | The Atiyah–Segal completion theorem |