Is there any hope of transferring into a more prestigious PhD program in a different field?(math to physics, or math to applied math) Are there any prestigious PhD programs that look favorably on an applicant who has already earned a PhD in a different field?
A little background for those seeking it:
I am currently a first year PhD student in pure math at a school ranked in the 20's. I had a very successful undergraduate education at a good liberal arts school which did not offer graduate classes and was very disappointed, but not particularly surprised, when I was rejected by my top 7 choices for graduate school. I felt my application was strong is all areas except graduate coursework, and perhaps personal statement.
After being rejected from the top schools for both undergraduate and graduate admissions, I am a determined to change my luck and trying to determine where to best focus my efforts. I'd like to stay in a pure math program if possible, but have been told that transferring to a program in the same subject is generally unsuccessful. I also have a strong interest in physics and as well as game theory and have a strong undergraduate physics background. I don't think I would be content staying in pure math my entire career and I hope to study these other fields in depth eventually. I am considering applying PhD programs in these subjects next year, or after I finish my current program. Are either of those realistic options?
I'm not particularly happy with my current school as far as location and fit, but chose it primarily because it was the strongest department that would have me. Since arriving I have succeeded in the few courses I have taken and have passed the qualifying exams. I'm hoping that this success significantly strengthens my application. I am searching for someone to start reading with, and I feel I should get my head straight on the issue of transferring, so I don't waste too much of any professor's time.
I would consider transferring to a program of similar strength if I felt better about the university as a whole. I'm content enough to continue my program here if I feel confident that if I excel I will be able to obtain a position that I am happy with, i.e. a top postdoc or a top PhD program in physics.
Sorry for the length. Thanks!