Fermions and the higher categorical separable closure of the real numbers

Abstract: In this talk, I will explain a sense in which the category of complex vector spaces does not have solutions to all "polynomial equations", and how adjoining such a solution leads to the category sVec of super vector spaces. Remarkably, a theorem of Deligne suggests that this category now is "algebraically closed" and is in fact uniquely characterized as the "algebraic closure" of the category of vector spaces. I will outline work in progress extending this to higher dimensions, leading to the higher categorical separable closure of the complex numbers. Constructing and analyzing it involves ideas from Galois theory, stable homotopy theory and quantum field theory. Based on joint work in progress with Theo Johnson-Freyd.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home