My math teacher gave us the following instruction: « Pick any subject of your choice (in math of course) and in 2 months present it to the class ».
I really like this idea, and I really like group theory hence I am looking for an interesting/intuitive subject in group theory which has visual results/theorems.
I know the basics of group theory: Lagrange theorem, Sylow theorems, group actions, the structure of finite abelian groups, Cayley graphs...
For example, I looked briefly at Lie groups and representation theory but this is far too complicated for me and I feel like there’s a huge gap between the above results and these two fields.
I’ve also looked at the braid group which is very interesting but it seems to me like there aren’t so many things that can be said about this group (except studying the word problem on this group).
Here is, briefly, what I know in maths: linear algebra (vector spaces, matrices, reduction, Jordan...), topology (only the topology of normed vector spaces), analysis (Riemann integration, ...).
Thank you in advance! (if you are not sure don’t hesitate to post suggestions in the comment section :) )