Geometric Tate-Swan cohomology of equivariant spectra
  We sketch a quick and dirty geometric approach to the Tate-Swan cohomology of equivariant spectra, illustrating it with conjectural applications to Atiyah-Segal $K$-theory of circle actions, and a possible geometric model for the topological cyclic homology of the sphere spectrum. 
Jack Morava
math.AT