Hamiltonian elements in algebraic K theory and the integers

Abstract: Much is known about algebraic K theory of the integers, in particular these groups are finitely generated. There is a secondary (or categorified) K theory of a commutative ring k, replacing finite type k modules by "finite type" A_infty categories over k. I explain how to get elements in this categorified K theory using symplectic geometry, and more basically Hamiltonian fibrations and the Fukaya category. As an upshot we can show that the categorified algebraic K theory groups of the integers are not generally finitely generated.