I am a PhD student in pure mathematics, and I want to work in the field of $C^*$-algebras and operator algebras I am looking for a relatively comprehensive view of this subject. For example,
- what are the mainstream areas?
- Who works on essential topics in the field?
- What are the main questions in these areas?
Of course, I like the geometric representation of these $C^*$-algebras and their applications in quantum physics, but by consulting with others, it's hard for a doctorate. I'm glad if anyone can introduce a resource or something that will increase my information.
PS : This question is my first question; maybe I have not entirely complied with the rules