Lars Hesselholt: The real additivity theorem

The classical additivity theorem states that, to the eyes of algebraic K-theory, the world looks semi-simple. The theorem of the title is the analogous result for real algebraic K-theory, which is related to algebraic K-theory as Atiyah's real K-theory is related to (topological) K-theory. In the first half of this talk, I will present a very elegant proof of the additivity theorem due to McCarthy, and in the second half, I will explain how Ib Madsen and myself have modified this proof to prove the real additivity theorem. The proofs apply in a very general context that includes (real) topological Hochschild homology.