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 |