Thursday 07 Nov 2019: NT Seminar: Doing algebraic K-theory algebraically
Dr Bernhard Koeck - University of Southampton
Higher algebraic K-groups are fundamental invariants of rings and spaces in Algebra, Arithmetic, Geometry and Topology. While their original definition, due to Quillen in 1972, involved homotopy theory, Grayson surprised the mathematical community in 2012 with a purely algebraic description in terms of generators and relations. This talk will explain this comparatively simple description and related results obtained in collaboration with Harris, Kasprowski, Taelman and Winges. For example, we’ll show how to purely algebraically construct exterior power operations on higher K-groups and prove that they satisfy the axioms of a special lambda ring.