UAlberta-PIMS Mathematics and Statistics Colloquium: Theo Johnson-Freyd

Not all quadratic equations admit solutions over the real numbers: You need to adjoin a square root of -1. Quite remarkably, once you do this, then *every* polynomial has a solution. I will explain a sense in which the category Vec_C also does not have solutions to all "polynomial equations". Quite remarkably, you *can* adjoin just a single "root of unity" to it to get an "algebraically closed category": the category of super vector spaces. This pattern continues: for each n, there is an "algebraically closed n-category" which is built from the modules over the previous case by adjoining some "roots of lisa@pims.math.ca unity". Constructing and analyzing it involves ideas from quantum field theory, stable homotopy theory, differential topology, and classical Galois theory. This is joint work in progress with David Reutter.