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:

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