TITLE: Is there active research in Galois Theory?
QUESTION [37 upvotes]: I recently decided to introduce myself to the field of Modern Algebra - in particular, Galois theory - and I found it absolutely beautiful! Thus I would really like to study something in Galois theory, which leads me to ask - do people still develop Galois theory? What else is there to learn in the subject?
I am inspired by questions like these:
What kind of work do modern day algebraists do? and What do modern-day analysts actually do? and would love to learn your opinions, stories, etc!
Thanks in advance!

REPLY [2 votes]: There are several generalizations of Galois Theory in progress. Some of them are of groups acting on commutative and non-commutative rings (other than fields), groups acting partially on rings, groupoids acting globally and partially on rings, and much more. We have a group of students and professors who work with that type of variants in my university (Federal University of Rio Grande do Sul - UFRGS). Some beautiful papers that you can look to know more about it (they are a little difficult, but are just examples of what you can do):
Partial groupoid actions: globalization, Morita theory and Galois theory
The Galois correspondence theorem for groupoid actions
Partial actions and Galois theory
A Characterisation for a groupoid Galois extension using partial isomorphisms
A Galois-Grothendieck-type correspondence for groupoid actions
Galois correspondences for partial Galois Azumaya extensions
Hope you enjoy it!