A homological approach to topological cyclic theory

The scientific focus of the project is on the category of Brave New Rings, or S-algebras. This is a topological enrichment extending the world of algebraic rings into a category which includes 'topological rings' like the sphere spectrum. The study of t hese brave new rings are important since they connect questions in various fields of pure mathematics to eachother. The algebraic K-theory functor is subtle invariant of S-algebras and captures much of their 'arithmetics'. The project proposes a way to supply more information about this invariant in the form of explicit computations of a closely related invariant, namely the topological cyclic homology of an S-algebra. The applicant will, under the proposed postdoc-position, stay and cooporate with mem bers of the algebraic topology groups at the École Polytéchnique Fédérale de Lausanne, Switzerland and at Stanford University, California, USA. Both groups are highly active in the field and will supply the applicant with a stimulating scientific researc h environment. The applicant aim at returning to Norway when the postdoctoral position has expired and continue collaboration with the group of algebraic topologists in Norway.