I have completed my Ph.D dissertation in Pure Mathematics this year from a relatively lesser known University. I have been through these questions like Considering a second PhD, this time in statistics. Will any professors be interested in working with me? and Is doing two PhDs a good path?.
However I am interested in pursuing a PhD again in another branch of Mathematics from a graduate school which is a very well known University.
The University where I want to apply does not have any age limit for pursuing a PhD. I want to shift from my current research field to another field as I have become interested in it recently. I also believe that getting a PhD from top-tier institution will increase my chances for getting a tenure track position.
My questions are:
How do I convince the interview committee that I want to complete another PhD in mathematics/Theoretical computer science as I am genuinely interested.
Also I enjoy remaining a student as long as I can. I enjoy taking courses and writing papers. Will that be also a valid reason to tell the interview committee.
My advisor feels that my chances of getting another PhD in Maths/TCS are slim since I already have a PhD and the interview committee would consider this as a waste of time and resource to hire me as PhD student again.
The problem is I don't like the fact that I will no longer be a grad student anymore. I like this whole concept of doing research and getting paid(though meagerly but it still suits me).
If someone could help me with my queries, I will be grateful.