Polylogarithms, K-theory, and the Steinberg module

In 1990, Zagier made a striking conjecture about special values of Dedekind zeta functions. In particular, Zagier’s conjecture predicts a direct connection between polylogarithms and the algebraic K-theory of number fields. The classical approach to understanding this connection, developed in the work of Beilinson, Deligne, Goncharov, and others, is based on the theory of mixed Tate motives. I will explain a different way to see this connection, using homotopy theory of general linear groups. The talk is based on a joint work with Ismael Sierra and Alexander Kupers.