Galois Category and Étale Fundamental Group

I’m in a good mood today because it’s my birthday 🎉 and I finally finished recording my final presentation for PMATH 965! For my final presentation, I did an exposition on Galois categories and étale fundamental groups. Here’s the Youtube video of my presentation, and you can download the slides here.

In a nutshell, first I gave some motivations from Galois theory and algebraic topology where I made an analogy between the fundamental theorems of Galois theory and covering spaces, I then explained some backgrounds on Galois category and finite étale morphisms, and finally I use these backgrounds to define étale fundamental groups.