Hermitian K-theory of stable infinity-categories

Abstract: The talk will give an overview of Grothendieck–Witt theory in the higher categorical formalism of stable infinity-categories equipped with a Poincaré structure. As an example of the flexibility of this framework, we will see how to relate the Grothendieck–Witt groups to Ranicki's $L$-groups and how to prove a strong version of Karoubi's periodicity theorem without assuming that 2 is invertible in the base ring.

This is joint work with Calmès, Harpaz, Hebestreit, Land, Moi, Nardin, Nikolaus and Steimle.

Mathematics

Audience: researchers in the topic

Opening Workshop (IRP Higher Homotopy Structures 2021, CRM-Bellaterra)