Hello Quantum Formalists,
Happy new year! The Group theory crash course is only four weeks away!:) Unfortunately, I could not find time to do the extra sessions I promised for the Topology & Differential Geometry crash course (e.g. fibre bundles)! However, I plan to return to this in the Lie groups section before covering the notion of 'Principal G-Bundle', where G is a Lie group.
Regarding the upcoming crash course, I've decided to start from the basics and take a layered abstraction approach as follows:
We'll begin lecture one with the notions of binary operations on sets, then define the notion of semigroup.
In lecture two, we'll cover monoids, submonoids and monoid homomorphisms etc.
Only in lecture three we'll start getting into groups!
I think the above approach is pedagogically friendlier in helping you get a good overview of how abstract mathematical structures such as groups are interconnected with other abstract structures. The registration page for the first lecture is now up https://www.crowdcast.io/e/group-theory-lecture-01.
Finally, to help me adjust the level of abstraction, please take this short survey (less than 60 seconds), so I can have an idea about your technical background: https://forms.gle/zhcTx29cVVqMHVVYA.
See you all on Friday, February 25 (5 pm BST)!
Bambordé