Mathematics Colloquium
Niles Johnson
The Ohio State University
Title: Algebraic K-theory for 2-categories
Date: Friday, March 25, 2022
Place and Time: Love 101, 3:05pm
Abstract.
Quillen recognized the higher algebraic K-groups of a ring R as homotopy groups of a certain topological space, BGL(R)+. We review some of the basic definitions and computations via categorical algebra. We then describe how a 2-categorical extension of this theory leads to a new model for K_3(R), together with more general applications. We will give a mild sampling of key technical details and close with some of the problems we are currently working on. The work we present is joint with Gurski-Osorno, Fontes-Gurski and Parab.