Lecture abstract

Time:   6. November 2019
Place:   Mathematical Institute
Title:   3-categories, 3-groups and higher gauge theory
Abstract:
We will describe the application of the cateogory theory formalism to fundamental physics. After a short introduction into the notions of 2-groups and 3-groups, we will give a step-by-step overview of the gauge theory construction based on a notion of a 3-group. This is an known as higher gauge theory, based on general ideas of Baez and Huerta. We will discuss which 3-group reproduces the Standard Model and Einstein-Cartan gravity at the classical level. The main novelty, compared to standard quantum field theory constructions, is that the 3-group structure features a structure intimately connected to the fermion and scalar sectors of the Standard Model. This could open new avenues for research on unification of all interactions and matter.