# Tom Bachmann: Cohomology of Eilenberg–MacLane spaces

**Time: **
Thu 2022-12-01 10.15 - 12.00

**Location: **
SU, hus 1, lärosal 2

**Participating: **
Tom Bachmann, Oslo

**Abstract**

Two decades ago Voevodsky determined the motivic Steenrod algebra: all bistable operations in motivic cohomology are generated by the motivic Steenrod operations that he constructed. He also remarked at the time that these operations do *not* generate the motivic cohomology of motivic Eilenberg–MacLane *spaces*. I will explain joint work in progress with Mike Hopkins where we determine these cohomologies. In particular we find the missing operations — somewhat surprisingly they just come from topology, no motives involved. Time permitting I will also talk about the motivic homology of free normed spectra, and the relationship between these two topics.