I am really in a fix in my career.
I completed my Masters in 2014. I qualified in a PhD Scholarships Test in 2015 and in the same year joined in a University for research work.
My interest lies in Linear Algebra, Topology, Abstract Algebra. My guide offered me to work in Spectral Graph Theory. As I was not quite acquainted with the topic I took up this topic for research.
As I am reading on my own, I am getting stuck on many theorems and some problems.
My guide has said recently that he does not have much expertise on this topic besides the preliminaries and hence he can't answer each and every problem of mine. He has said that the topic is new to him also. I have found now that also does not have any research papers to his name on Spectral Graph Theory as well. I was not aware of this before
My question is how important is the choice of a guide/adviser for pursuing PhD in a topic and what needs to be checked before joining him.
Is it wise continuing to work with him or should I look for some alternatives. Does getting a PhD depend a lot on your guide or I am expecting a lot from my guide? Does pursuing a PhD mean you have to do all along yourself?
I know there are many in this site who have got a PhD or have served as guides/advisors for many students. Please help. Any suggestions will be helpful. I would be happy to give more inputs if required.