I have a solid understanding of the basics of expander graphs and their properties and the recent development of High-Dimensional Expanders and their application to Random Walks, along with other stuff like Local-to-Global Theorem. As they progress, I feel there is ever strengthening connection between Representation Theory of Lie Groups, HDXs and Number Theory.
Although it might be too wide to list down all the 'prerequisites' to understand these modern developments, as a yearning TCS guy, I would love to get a glimpse of the possible steps one must take to understand these modern developments. Since these are quite recent, I haven't had any luck finding comprehensive lecture notes that are able to at least summarise the connections well.
I would love if someone could give me possible steps that I could take to get a better understanding about some of the modern developments in the field. Some of the representative examples would be High-dimensional expanders from Chevalley groups , Isoperimetric Inequalities for Ramanujan Complexes Bourgain-Gamburd-Sarnak Machine
I have taken a basic course in representation theory, but that didn't touch Lie Groups at all. Apart from that I have basic Algebraic Topology Knowledge and have done a course in Algebraic Number Theory.
Some possible starting points that I feel are worth looking are the Property (T), Geometric Group Theory, Metric Spaces of Non-positive Curvatures and maybe building upto Bruhat-Tits Building. This is a passion project for me, so I don't mind taking detours and going from the basics, so do let me know if I'm way out of my depth (I hope I am) and what foundational stuff I should be looking into.
Any help would be really appreciated!