Basically, I am a senior and applying to physics programs, but don't have a set research area of interest.
Recently, I've become more interested in mathematical physics, and applied math.(for instance PDEs / dynamical systems). I may be interested in high-energy theory, and more "high end" theoretical, but right now I'm just interested in applied math in general.
It seems to me a new way is emerging to pursue theoretical physics, which is go to graduate school in mathematics.
Currently, I'm planning on applying to physics programs, as I don't feel prepared to apply to math programs and am still unsure about doing a PhD in math.
Here are some questions:
Is it possible to do doctoral research with math faculty, and get a Physics PhD?
How hard is it to transfer from physics grad school to math grad school? (within the same university). Any chance my course credits from physics would transfer?
What are your general opinions on math research?
I know there is some really neat research going on at my school, regarding topics such as renormalization, chaotic systems, and even gauge theory. But I didn't find out about it until end of my 3rd year here.