### WiSe 20/21 Oberseminar: Hermitian K-theory for stable ∞-categories

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

The goal of this seminar is to study the foundations of Hermitian K-theory recently developed by Calmès, Dotto, Harpaz, Hebestreit, Land, Moi, Nardin, Nikolaus, and Steimle. They associate a genuine C₂-spectrum to any stable ∞-category with a nondegenerate quadratic functor, whose underlying spectrum is K-theory and whose geometric fixed points is L-theory. Their construction has good formal properties whether or not 2 is invertible and leads to the computation of the Hermitian K-theory of the integers.

We will cover the general theory of Poincaré ∞-categories and the construction of Hermitian K-theory, following the papers:

*Hermitian K-theory for stable ∞-categories I: Foundations**Hermitian K-theory for stable ∞-categories II: Cobordism categories and additivity*

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

03.11 | Denis Nardin | Introduction |

10.11 | Ulrich Bunke | Hermitian and Poincaré ∞-categories |

17.11 | Luca Pol | Poincaré objects and L-groups |

24.11 | Brian Shin | Poincaré structures on module categories |

01.12 | Joel Stapleton | Examples of Poincaré ∞-categories |

08.12 | Lucy Yang | The ∞-category of Poincaré ∞-categories |

15.12 | Vladimir Sosnilo | Poincaré–Verdier sequences and additive functors |

22.12 | Marc Hoyois | The hermitian Q-construction and algebraic cobordism categories |

12.01 | Christoph Winges | Structure theory for additive functors |

19.01 | Elden Elmanto | Grothendieck–Witt theory |

26.01 | Gabriel Angelini-Knoll | The real algebraic K-theory spectrum |

02.02 | Fabian Hebestreit | Comparison with group completion |