Sander Kupers - Algebraic K-theory and the unstable homology of general linear group

The stable homology of general linear groups over a field is well-known to be closely related to its algebraic K-theory. I will discuss joint work with Soren Galatius and Oscar Randal-Williams which investigates the unstable homology of general linear groups. We will find it is closely related to the Milnor K-theory, by constructing a presentation of the disjoint union of BGL_n(F) as an E_\infty-algebra.