Chromatic polylogarithms

Polylogarithms are analytic functions whose special values are related to Dedekind zeta functions. This suggests that special values of polylogarithms should come from motivic classes in algebraic K-theory. Such motivic classes, at least with some technical assumptions, were indeed first constructed by Beilinson, Deligne, and Soulé. In this talk, I want to explain a new construction of the polylogarithm functions in algebraic K-theory and in motivic cohomology, which naturally recover the motivic classes of Beilinson--Deligne--Soulé, and which also suggests a surprising relation to chromatic homotopy theory. This is a joint work in progress with Arpon Raksit.