T.B.A.
The lecture course addresses all investigators in the CRC whose projects are concerned with K-Theory.
The goal of the lecture is to explain the recent notion of continuous K-Theory and its relation to geometric topology. We will also cover Verdier duality, microsupport theory and six-functor formalisms for the categories of sheaves of spectra/chain complexes on topological spaces. Key is the recent formalism of locally rigid and dualizable stable infinity-categories (a la Gaitsgory-Rozenblyum, Lurie, Efimov, Clausen, ....). Part of the course will be an introduction to these abstract concepts. Also the shape of a topos will be relevant, which can also serve as the basis of étale homotopy theory (on demand we can cover basics of that as well). We plan to write lecture notes that will be made available here.
We will assume some familiarity with infinity-categories, but try to avoid overly technical details.