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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,

  1. what are the mainstream areas?
  2. Who works on essential topics in the field?
  3. What are the main questions in these areas?
  4. ...?

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

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closed as off-topic by Parcly Taxel, Ernie060, achille hui, YuiTo Cheng, Javi May 26 at 10:33

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Seeking personal advice. Questions about choosing a course, academic program, career path, etc. are off-topic. Such questions should be directed to those employed by the institution in question, or other qualified individuals who know your specific circumstances." – Parcly Taxel, Ernie060, achille hui, YuiTo Cheng, Javi
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ It's very rare that I get the opportunity to say this on here, but this actually might be a better question to ask the nice folks over at mathoverflow.net -- they're basically just like us here except with a focus on research-level mathematics. $\endgroup$ – Jack Crawford May 26 at 10:15
  • $\begingroup$ @JackCrawford thank you very much. I was also hesitant to ask this question here or not. Thanks for the guide $\endgroup$ – erfan soheil May 26 at 10:23
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    $\begingroup$ I would suggest that you ask your PhD advisor instead. Neither here nor MathOverflow is a good fit for this question $\endgroup$ – davidlowryduda May 26 at 12:47
  • $\begingroup$ @davidlowryduda, thank you very much $\endgroup$ – erfan soheil May 26 at 20:23