Stavros Tsalidis: `Topological Witt homology and topological cyclic homology'.

We will define the notion of a special symmetric monoidal category, and consider symmetric monoidal functors F from such a category to the category of based spaces with smash product as its monoidal operation. Particular cases of such functors F are the FSP's introduced by Bökstedt, as well as J. Smith's symmetric spectra. Given such a functor F and a topological group G, we construct a cyclic spectrum whose geometric realization is called here the topological Burnside-Witt homology of F. Applying this construction with F an FSP and G a finite cyclic group, one gets the G-fixed points of the Topological Hochschild homology spectrum of F, as defined by Bökstedt. Further properties of the Burnside-Witt construction will be recounted if time permits.