Theoretical Non-Physics Seminar: David O'Connell

This is the 33rd biweekly session of the OIST Theoretical Physics Seminar.
In this seminar series, we pretend to have a theoretical physics department, and tell each other informal stories over drinks and snacks.
Except no drinks and snacks, because people stopped consuming them for some reason. If you want them back, let me know.
And except this time it's more math than physics. But it's relevant math, so OK.

Speaker: David O'Connell (Quantum Gravity).
Title: "Principal G-Bundles".

It is commonplace in mathematics to ask whether meaningful combinations of various structures exist (and make sense). So far in 2021 I have talked about two seemingly-unrelated classes of structures, namely Lie groups and Vector bundles. In this talk, I will introduce the rather aesthetic combination of the two ideas, a collection of objects known as Principal G-bundles. Aside from being pretty cool, these special objects serve as the geometric foundation of electromagnetism and Yang-Mills theories. 
We will start with a brief recap of the various relevant background, and then we will slowly develop the basics of the theory. As usual, I will try my best to make this talk as self-contained as possible.