Title: The Galois action on symplectic K-theory

Abstract: Interesting Galois representations occur in the cohomology of arithmetic groups. For example, all Galois representations attached to elliptic curves over Q arise in this way. It turns out that arithmetic geometry can be used to construct a natural Galois action on a type of invariant called algebraic K-theory, which is closely related to the stable homology of arithmetic groups. I will explain this and joint work with Akshay Venkatesh and Soren Galatius in which we compute the Galois action on the symplectic K-theory of the integers.